One of the problems with FTTL is that the output can source sink a lot of current and the transitions are fast. In the mid 80s and even on PCBs with normal decoupling, that became a problem when several outputs were switching simultaneously, especially when driving transmission lines or above normal capacitance.
The cause was the currents during the transitions caused ground bounce inside the IC. For simple buffers that manifested itself as crosstalk, glitches and increased delays. For circuits containing state (registers, counters), the state could be flipped. The TC is a combinatorial output derived from all the counter outputs. The OP mentions TC giving a "short pulse", but doesn't compare that to the clock period. It is thus possible that internal ground bounce is flipping some/all counter outputs asynchronously, which would mess up the preset operation.
The OP hasn't mentioned the construction techniques. Since even PCB construction are known to be problematic, if he is using a solderless breadboard then I doubt he will get this to work as expected.
For the avoidance of doubt, any such problems would occur even with a 1Hz clock. The clock frequency is irrelevant, only the transition time and lead inductance is relevant.