Remember that, once you JMP from a Stage, one final pass is made on the next scan to turn off any outputs which are the object of an OUT. The 'turnoff' scan of S1 will be doing that nullifying the effect of S2.
As a test in S2 add a second rung copying the state of Y0 and C0, by means of a SET, to another pair of memory spots. E.g. RST C2, C3, STR Y0, Set C2, Str C0, Set C3
Edit - I added the RSTs of C2 and C3 to the end of S2's first rung. The two conditional SETs were one rung each.