The gemara struggles to figure out a way how reuven can be makneh his money that he has at home to shimon, who will then use that money to redeem the ma'aser sheini of reuven and avoid the extra fifth penalty. The gemara suggests that had reuven had property to be makneh to shimon, he could be makneh the money "agav" the property. Although Tosafos in baba kama 12a writes that kinyan agav is only d'rabonon, apparently tosafos understands that even a kinyan d'rabonon would be sufficient to establish shimon as an owner of the money to redeem the ma'aser sheini and m'doraysa avoid the extra fifth penalty.
Tosafos raises a question: Even without a kinyan agav or kinyan sudar, can't reuven very directly be makneh to shimon the money by "admitting" that it actually belongs to shimon? In this question Tosafos assumes that a hoda'ah doesn't merely allow beis din to act as if witnesses testified, but it actually transfroms the ownership of the item to belong to shimon and would be considered shimon's money for ma'aser sheini redemption purposes. The Ketzos HaChoshen (40) answers Tosafos question by establishing a clause in this type of kinyan that it must be done in the presence of witnesses. Therefore, we can easily make the case where there are no witnesses available to allow the kinyan hoda'ah to go into effect (the ketzos confirms this point based on tosafos in kiddushin who proves from this gemara that a kinyan sudar does not require witnesses to make the kinyan go into effect, from the fact that the gemara didn't say that kinyan sudar wasn't an option due to a lack of eidim).
Therefore, the ketzos (194:4) has an elaborate discussion where he explains that this type of admitting would serve as a kinyan even for the purpose of transfering chometz that is another place to belong to a goy. We see from the fact that it works for ma'aser sheini that it not only works for monetary purposes but even for issur purposes, therefore it should work for chometz as well. But, Tosafos in Baba Kama 104b implies that it would not work on a d'oraysa level and wouldn't work for ma'aser sheini purposes. Nevertheless, the ketzos argue that it should still work for chometz since one as mevatel the chometz and the requirement to rid themself of it is only d'arbonon. But in truth the ketzos points out that even if kinyan hoda'ah is only rabbinic in origin, it shouldn't be any worse than kinyan agav which works for ma'aser sheini.
I would suggest that tosafos in baba kama doesn't necessarily contradict our tosafos because tosafos in baba kama is speaking about admitting that you own property by which you will be makneh the money through a kinyan agav - to which tosafos says that it doesn't work for a d'oraysa. But our Tosafos speaks of directly being makneh the money through admitting which would work for a d'oraysa. The rationale for the distinction is that admitting to owning property would require 2 derabonons - 1 for the kinyan hoda'ah and 2 for kinyan agav. A kinyan which is based on a combination of 2 d'rabonons is weaker and won't work for a d'oraysa - maybe?