Whenevent how to use Mod multiple times

I need to use Whenevent inside NDSolve. The event is formed by Mod[t,ST1] && !Mod[t, ST2]. I’ve already read the documentation and previous questions about how Whenevent manages the event trigger.
What I need is that the action happens when Mod[t, ST1] is True but not when Mod[t, ST2] is True. Here is a simple code to represent the issue:

eqTime = {time'[t] == 1, time[0] == 0}; update = WhenEvent[Mod[t, 0.1] && !Mod[t,0.2], { a[t] -> a[t] + 0.1, Sow@a[t]}]; (*Not Working*) ic = a[0] == 0; {sol, data} =    NDSolveValue[{eqTime, update, ic}, a[t], {t, 0, 1},      DiscreteVariables -> a[t]] // Reap;  Plot[sol, {t, t0, 1}] 

The output should be a step function that increases at {0.1, 0.3, 0.5, 0.7, 0.9} which should also be the list stored in data variable.