The gemara learns out from the pasuk of בפיך that there is a violation of בל תאחר for delaying the tzedaka that one owes to the poor. Rava says that the violation of בל תאחר is immediate since there are aniyim available. The gemara elaborates that even though it is learned from the context of korbanos, it is not dependent on the passing of 3 regalim like yom tov, rather it is immediate. The definition of לאלתר - immediate, is somewhat nebulous. It seems from Tosafos on 4a that it is one regel (and that even tzedaka is dependent on the regel). However, the language of לאלתר seems to imply literally מיד as is recorded in shulchan aruch Y.D. 557:3, which would probably mean at the earliest opportunity that is feasible.
The Braisa on 4a lists tzedakah as one of the items for which there is בל תאחר after 3 regalim. All the Rishonim raise the question that this contradicts the statement of Rava who considers it to be immediate. There are 3 approaches in the Rishonim that are cited by the Gr"a in Shulchan Aruch 557:6.
1. Tosafos 4a holds that when there are aniyim present, the violation is immediate which is clearly what Rava was speaking about. When aniyim aren't present one has 3 regalim to distribute the money. Meaning he has the obligation to seek out the aniyim before the expiration of 3 regalim. The implication of Tosafos at the end is that the definition of "immediate" is until the first regel passes.
2. The Rashba holds like the approach that Tosafos rejects. The aseh is violated immediately, but the lo ta'aseh is only violated with the passing of 3 regalim. He holds that even in the absence of aniyim one is in violation with the passing of 3 regalim.
3. The Ran (and Rambam) hold that tzedaka is only mentioned derech agav in the braisa. The entire obligation is contingent on the presence of aniyim. When aniyim are present one is in violation immediately. When they are not present, there is never an obligation to track them down and even after 3 regalim pass one would not be in violation of בל תאחר.
The Shulchan Aruch 557:3 paskens like the Rambam and Ran. The Gr"a agrees with this approach as well because the concept of being dependent on the regel is simply because that is when people were in yerushalayim and were able to bring their korbanos. There is no inherent connection between בל תאחר and the regel. Therefore, tzedaka is no at all connected to the regel, it is completley contingent on the access to aniyim. Nevertheless, the Shulchan Aruch and Rambam write that since one is capable of separating the money even when aniyim aren't present, they are required to at least separate it from their regular spending money and put it in a designated account for the aniyim.
Regarding pledging money to a shul or organization, the Rama writes that the בל תאחר only applies once they send a bill claiming the money. When receiving the bill, it must be paid immeditately. The Rama also writes that one is obligated to tell the gabbai that he made a pledge so that a bill can be sent. Finally, the Rambam and Shulchan Aruch conclude that if a person stipulates that they will distribute their tzedaka at will, and not be bound to give by a certain time, they avoid bal te'acher.