Cross-lagged model and supplement regressions: Do I have to include my control variables in the supplement regression analyses?

I’m conducting a cross-lagged panel model with 3 measurement waves. I include my two main variables (act, ese) and control variables (cv1, cv2, cv3).

I also run supplement regression analyses to assess the effects for the measurement waves individually. Do I have to include my control variables in the supplement regression analyses as well?

Lagged Model:

lme(act2 ~ time + cv1 + cv2 + cv3 + act + ese, random=~1|ID, data=data_long_lagged)

Supplement Regressions (for act2 across 2 time periods):
lm(t2_act ~ t1_act + t1_ese)
lm(t3_act ~ t2_act + t2_ese)

My question: Should I include cv1+cv2+cv3 as control variables in the supplement regression models?

Thanks a lot!