The Turei Even wonders why the gemara did not entertain the possibility that Rav Papayus was talking about a year in which Shavuos fell on Shabbos. Since the Yom Tov of Shavuos is only one day, and it would have been impossible to offer a voluntary korban offering on that one day if it fell on Shabbos, that would cancel any penalty for delaying. You can’t be liable for bal t’acher if there is an issur of bringing the korban!
The Turei Even answers that since with respect to korbanos there is tashlumin for seven days, i.e. if someone did not bring their olas re’iya on Shavuos, they still get a week to make it up, viz a viz voluntary korbanos as well, the entire week, not just the first day, counts as being part of the regel.
R’ Wahrman in his She’eris Yosef (vol 2) points out that the shakla v’terya of the Turei Even raises a fundamental question about the nature of tashlumin: is tashlumin an opportunity to bring korbanos ha’chag once the chag has passed, or is tashlumin an indication that to some degree the cheftza of Yom Tov, the kedushas ha’chag, lingers and has not passed, even though there is no issur melacha?
If the chag is over, then then bal t’acher should not apply to korbanos which could not be brought on the first day. But if tashlumin is an extension of Yom Tov, then even if one could not bring korbanos nedava on the first day, one would be liable for bal t’acher for failing to do so on the remaining tashlumin days, as it still counts as if one had the opportunity to bring the korban on Y"T.
This question may be behind the different minhagin as to whether tachanun is said in the week after Shavuos. If the chag is over and tashlumin is just a korbanos make-up opportunity, then tachanun should be said. If tashlumin means the chag itself continues, then it would seem that there is more license to omit tachanun.