That verse definitely reinforces your point and it underscores that sojourners are to be treated as native-born. It is one example of how they are to be treated.
Given that it's a tithe that goes to Levites first, it is certainly to be understood in terms of involvement with the Jewish religion and culture. Therefore, for the sojourner to participate would mean an acceptance or comfortableness by the foreigner of the culture and religion of Israel.
In other words, we not dealing with a military invasion, or the presence of a criminal element, but with a person seriously seeking to reside peaceably in the country...and even to fit in.
IOW, cartel members, drug runners, operators of schemes, con artists, fugitives, etc., are not really seen in the picture of the foreigner sharing in the tithe with the Levite. A worker with his family, his kids in school, and his feet in church IS seen in that picture.