The current implementation of timers in ROS (1 and 2) doesn’t support this feature. Imo this seems to be very specific and I think it is reasonable to implement that on top of the existing API.
You should be able to create a ROS package (or maybe multiple: one for C one for C++?) which provides this additional API. Your API would use “normal” ROS timers and in the first interval adjust the duration to happen at the full minute. Any following timer will then be with a fixed duration.