I've never read details on what it was like for the first black Representatives and Senators in Congress, but given that they were appointed to southern seats during reconstruction, I always assumed the situation was similar to what you wrote. Hiram Revels, for example, was appointed to Jefferson Davis' old Senate seat in Mississippi, basically to give the middle finger to supporters of the confederacy. I doubt it would have been safe for him to return to Mississippi during his Senate term. If it weren't under those circumstances though, I think most of the citizens of Mississippi and the other reconstruction states would have been pleasantly surprised by the new black Congressmen, most of them turned out to be excellent public officials and voices for reconciliation in the south. It's interesting to note, however, that South Carolina's Joseph Rainey stayed in Congress until 1879, though reconstruction ended in 1876. He must have been very popular with his constituents to continue to be re-elected even after reconstruction.
It’s really hard to tell how good (or bad) those Black members might’ve been, if only because they served such a brief period. Hiram Revels served barely a year in office (by the way, he did not occupy Jefferson Davis’s seat, Blanche Bruce did). The MS legislature chose to elect the White Republican Governors Adelbert Ames (a New England Carpetbagger) and James Alcorn (a Southern Whig turned Confederate turned Scalawag) to the Senate seats (Alcorn to the full 6-year term that Revels vacated; Ames to the Jefferson Davis seat).
BTW, the “end” of Reconstruction in 1877 (due to the deal Rutherford Hayes cut with the Dems in order to get the Presidency, which would’ve been ended regardless with a President Tilden) didn’t mean the end of Black officeholders. It largely meant the end of their being able to influence statewide contests and the like. In reality, there were still pockets of power in the South that lasted up until about 1900.
The coastal SC district Joseph Rainey represented was Black majority and elected Black Republicans as late as 1894 with George Washington Murray (who had to be seated after a contested election and served until March 1897). Only with the forceful implementation of Jim Crow were the last vestigates of Republicanism in that state wiped out. Just to get an idea in the SC 1st (which Rainey and Murray represented). Murray’s numbers dwindled from 3,900 votes in 1894 (which was 53% of the vote once the fraudulent Dem votes were tossed out) to 2,500 votes in 1896 (34% of the vote against the White Dem who stole the prior race) to 1,500 votes (also 34%) in his final race in 1898. Another Republican ran in 1900 (his race I don’t know), and he got 1,400 votes (27%).
But in 1902 marked when the SC GOP candidates were desultory, averaging anywhere from 600 votes to 30. Not until 1944 would another candidate get over 1,000 votes (7% of the vote), and not until the special election in 1971 following the death of Mendel Rivers, would the GOP legitimately contest the seat (where future Governor James Edwards got 41%). Tim Scott, btw, represents Georgetown, which was Joseph Rainey’s hometown (even though Rainey stayed in DC for a time, he did retire to Georgetown in the post-Reconstruction period, died there, and was buried there, though he was a relatively young 55).
North Carolina was partly similar to SC, and they also had Black Republicans representing the coastal 2nd district on and off clear up until 1901 (with George White being the last), which is now mostly the Black 1st today. Unlike SC, where most of the White participation vanished at the end of Reconstruction, the NC GOP enjoyed a resurgence in the 1890s while making common cause with the Populist movement (in other Southern states, such as SC, the Populists were part of a faction with the Democrats battling against the Bourbons — but in SC, were bitterly racist, as exemplified by Pitchfork Ben Tillman).
The horrified Democrats in NC seeing the GOP-Populist coalition majority went to exceptional lengths to destroy it, and were able to do so by 1900, in massively disenfranchising the Black Republicans, leaving just the Mountain Republicans with a handful of Piedmont Republicans to win occasional races thereafter. The infamous Wilmington Riots of 1898, where there was a biracial Republican city government, exemplified that Democrats were not above launching a coup d’etat and running the legitimately elected officials out of town on a rail.
You’ll note the numbers I cited above for SC races, which had a paltry turnout. Contrast it with George White in the NC-2nd, who received almost 20,000 votes in his first win in 1896 (52%). Black turnout was estimated at 85% because the laws with respect to suppressing their vote were repealed by the legislature when the GOP obtained power (however briefly).
He still got almost 18,000 votes in 1898 (but 49.5% of the vote). But with Jim Crow taking him out of the running for 1900, a White Republican ex-Congressman who had won in the 1st district back in 1878 was the nominee, and he got almost 14,000 votes (37%). By 1904, Republican participation had been decimated by almost 90%, and nominees would be lucky to get 13% of the vote (rarely more than that). Not until 1966 would a Republican get more than 30% of the vote in that district (interestingly, Eva Clayton ran against Congressman Lawrence Fountain in the 1968 Dem primary, getting 1/3rd of the vote. She’d wait another quarter century before winning a seat of her own).
White himself left North Carolina and moved to Philadelphia. He actually tried running for Congress again in 1912 in PA-1 (presumably in the special election when longtime Republican and Civil War hero/Medal of Honor winner Henry Bingham died). I couldn’t specifically document in what capacity he ran, so it’s possible his name was floated and he withdrew, since the powerful GOP boss William Vare demanded and got the seat. Still, relying on GOP patronage, he secured two different positions before his death in 1918.