differential equations – 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.