I am now back from vacation and will iy"h be more consistent.
The gemara brings the machlokes between Rabba and Rav Yosef whether a finder of a lost object would have the status of a paid watchman who is responsible for theft. Tosafos discusses whether we pasken like Rabba or Rav Yosef, but explains that all agree that if a poor person would ask for tzedaka, you would be exempt from giving tzedaka during the time that you are busy caring for the lost object. The machlokes is only whether this benefit would cause the finder to assume a status of a paid watchman, or perhaps since it is not likely to happen, it wouldn't change the status of the finder.
The Maharatz Chiyus asks that the concept of osek b'mitzvah patur min ha'mitzvah only works to exempt a person from a positive commandment, but doesn't entitle him to violate a negative commandment. Tosafos in Baba Basra 8b says that by tzedaka there is a negative commandment as well and therefore doesn't qualify as a mitzvah aseh that has the reward of the mitzvah written next to it (and we are therefore able to use physical force to make him fulfill the mtizvah) - so how can we apply osek b'mitzvah to exempt him from tzedaka? I discussed this question in Nasiach B'chukecha (page 59) and quoted a brilliant answer from Rav Zalman Nechemia Goldberg. The Ramban in Kiddushin 34a says that sometimes a negative commandment only comes to support a positive one, but is fully bound by the rules of the positive mitzvah. Here too, the lo ta'aseh of tzedaka is only a support of the aseh, so when he is osek b'mitzvah and there is no aseh, there is also no lo ta'aseh applicable. But, in the context where one is actually in violation just that the beis din must decide whether they should administer punishment, since a lo ta'aseh is also violated, we don't consider this a mitzvas aseh sh'matan se'chara b'tzidah.
Tosafos assumes that according to Rav Yosef that the finder would have status of a paid watchman, he would be considered to be receiving benefit from the mitzvah. Tosafos asks why we would permit someone who swore off benefit from someone else to blow shofar for him (rosh hashana 28a), since at the time he would be exempt from tzedaka, he would be receiving a real benefit from the person he is blowing for? Tosafos answers that one who is taking care of a lost object is continuously busy with it, therefore it is likely that while he is busy, a poor man would come and ask him for tzedaka, and the benefit of being exempt would give him status of a s paid watchman. But when a person is blowing shofar for another, it is unlikely that a poor person would come at the time and therefore wouldn't be considered a real benefit.
Tosafos wrote on the previous amud that all agree that you would be exempt from giving a tzedaka while taking care of the lost object. Why does Tosafos only ask according to Rav Yosef, even according to Rabba he would be patur from giving tzedaka and benefiting? Simply, we can answer that according to Rabba who doesn't consider this common enough to render him a paid watchman, it also isn't common enough to consider it a benefit. However, perhaps the distinction is deeper. According to Rav Yosef we associate the benefit that the finder receives with the one who lost the object as he were actually paying him. Therefore, in a case of mudar ha'na'ah we should also consider the blower to be benefiting from the one who he is blowing for. However, according to Rabba, although the finder receives some benefit from the object, we don't associate this to be a benefit received from the loser to render the finder a paid watchman. Therefore, if the one would blow shofar for a mudar ha'na'ah, although we would consider the blower to be benefiting if a poor person would ask for tzedaka, this benefit is not considered to be a benefit from the one who he is blowing for and therefore permitted. Based on this, it would come out that there is a nafka minah between rabba and rav yosef if a poor person would be coming to ask for tzedaka while a mudar hana'ah is trying to blow shofar. According to Rav Yosef who must come on to Tosafos answer, you would be required to stop blowing to prevent receiving benefit, but according to Rabba we wouldn't consider this to be a benefit received from the one whom he is blowing for.