Yevamos 47a - Accepting Mitzvos

The gemara mentions that we have to tell the potential convert about mitzvos "some light mitzvos and some stringent mitzvos", when he accepts we then do milah, wait for it to heal, then do tevillah and once again tell him about "some light mitzvos and some stringent mitzvos", he then leaves the mikvah and is a full fledged Jew.

It is not so clear to me at which stage he actually is doing the kabalas hamitzvos. The gemara explains that the first time we tell him about mitzvos it is for the purpose of a deterrent, to try and get him to change his mind from conversion (Meiri points out that even telling him the light mitzvos serves as a deterrent bec. it implies that the religion is about insignificant details). This would indicate that the first time we tell him about mitzvos it is not for the purpose of a true kabalas hamitzvos. Furthermore, Rashi seems bothered by this and comments that the real kabalas hamitzvos must take place while he is in the water at the very last stage, as he is about to become a jew. A further proof that the kabalas hamitzvos occurs the 2nd time, not the first, is that the gemara only mentions the 2 talmidei chachamim (which is really 3 as the gemara clarifies) who serve as the beis din are only involved in the later stage. Tosafos 45b explained that the function of the beis din is for kabalas hamitzvos (not tevilla), so it seems clear the the kabalas hamitzvos is really happening the second time, not the first.

Why then does the gemara say "kibel" - if he accepts then we do milah, which implies that the kabalas hamitzvos is before the milah? Perhaps that "kibel" simply means that he wants to continue but does not formally do a kabalas hamitzvos in front of a beis din.