Two ideas:
First, slightly simpler, but more problematic, perhaps, for the story line: instead of removal of a drug that keeps it dormant, you could have your brilliant geneticist engineer in some sort of trigger. Anything, really, that could get into the blood stream and bind to receptors your virus sticks on the infected cells, which then trigger the virus to move into the next stage. Of course, this would then have to be delivered en masse (tampered water supply?)
The other idea is self-contained: your geneticist could engineer in some kind of counter for cell division, and have a trigger based on increasing concentrations of that. I once saw a model for an idea about this (the counter, not the nefarious part!), but it had some holes--like in reality the thing would probably count an indeterminate number of times each division, instead of just once. Although, I suppose it couldn't be too much more than 5-10 times or so, so if you were willing for some variation in trigger times, that isn't too far fetched. I'm not sure what cells you'd want to infect for this -- it would have to be something that divides at some regularly expected intervals, and that goes beyond my expertise. But I'm sure somebody knows that. If you want to go with something like this, you could use a quorum sensing circuit to respond to the increasing concentration -- these are feedback loops that trigger a self-sustaining behaviour once a certain concentration of the quorum signal is reached.
Hmm. You might be able to do the whole thing with quorum sensing -- just have your nasty emit some small signal that triggers a quorum sensing circuit, and as the number of infected cells increases, eventually there will be enough signal to have it move into phase two. This is how many virulent bacteria work -- they only express virulence factors when their quorum circuits are triggered by high concentrations of signal, so only go virulent when in large numbers.
Packing all this into a tiny viral genome could be tough, but presumably your brilliant geneticist can figure that out. Or, if it fits with the story to have a whole bacteria being the infective agent, you wouldn't have to worry about picking an infective target and could engineer in all sorts of bells and whistles...