Sync reset with push-button not reliable

always @ (posedge CLOCK_50)
  if (!rst_n) begin
    a3 <= 4'b0;
    a2 <= 4'b0;
    a1 <= 4'b0;
    a0 <= 4'b0;
  end
  else if (trigger & !done & ms_timeout) begin
    a3 <= a3_next;
    a2 <= a2_next;
    a1 <= a1_next;
    a0 <= a0_next;
  end

You have stated that above code implies synchronous reset.

but is your reset signal itself synchronised from origin?

Synchronous reset is true only if it is sourced synchronously. Applying it synchronously is not enough by itself. It may for example bounce at the key in your case.

Also mak sure that timing is not violated and you may delete your signaltap file and restart fresh.