In my SB church, this requirement for membership can be satisfied either with a letter from a previous church of like faith, or by a statement of faith by the candidate. It seems to be consistent with Romans 10:9 -
That if you confess with your mouth, "Jesus is Lord," and believe in your heart that God raised him from the dead, you will be saved.
As for the process of being saved, Baptists believe there is no process, but that salvation is once and for all complete at the point when the believer (through confessing need and the identity of Christ) accepts Christ as Lord and Savior into his/her heart.
The Rom 10:9 verse you quote is in the future tense. But you interpret it in the present (why am I not surprised!). This is the problem with non-Apostolic assemblies: everyone picks and chooses the verses that suit their particular brand of faith, their own personal version of Christ, their own private definitions and private interpretations, etc.
Consider then "but he that endureth to the end shall be saved" (Mat 10:22)
Salvation is something that has not yet occurred. Accepting Christ as your Savior is only the beginning of the process of salvation. It is a ticket...and it's up to you to jump on that train and stay on course until the end, living the faith (and that is more than going to bible reading every Sunday).
Baptists accept Christ and say they are instantly saved. And Luther basically said, "Praise the Lord, let it all hang out." You guys never cease to amaze me.