A second temporal dimension being shown doesn't automatically infer an uncountable infinite number of timelines.
It just has the capacity, or size, to hold that many.
Temporal dimensions are generally assumed to be infinite; time doesn't have a defined starting or stopping point.
To quote the
FAQ,
There are some disqualifiers that may prove a temporal dimension is not infinite, but that is somewhat atypical.
Low 1-C requires an infinite 5-dimensional container.
MWI Theory is necessary to prove a 5-D spatial axis is infinite because space is not assumed to be infinite.
You are proving that a 5-D spatial axis of infinite size must exist due to the size of the cosmology necessitating it.