Pretty much the same. There is one little twist.
The same rule about the runner being safe until appealed for the miss applies. And, the umpire there should also signal "safe" on the first pass of the base.
The twist is that pro rules have the concept of "relaxed" versus "unrelaxed" action. Basically, "relaxed" action means that the runner is past the base and making no immediate effort to correct his miss. The fielder can tag either the base or the runner for the appeal.
"Unrelaxed" action means that the runner is making some effort to quickly return, scramble back and touch the base. In that case, the runner himself must be tagged, not the base.
This concept of "relaxed" and "unrelaxed" action applies to all misses of not only first base, but also at home plate. Note that those are the only two bases that may be legally overrun when advancing.
(No way am I claiming to be a "pro" umpire! The above is from my copy of "The Rules of Professional Baseball", a text book that was used in one of the pro umpire schools from which MLB culls its recruits.)