I was in a similar situation before, I found out that drivers are on minimum wage and do not stick to office hours. Their employers usually summon them whenever they wish. So they will welcome tips and it might be a real help for them actually.
The employer was a friend/colleague, and I noticed that she tipped him, he buys the stuff with his own money (coffee or something) then when she pays him back she gives a little more (10 or 20 pesos).
When I was with the driver alone (twice) running my private errands, I tipped him at the end of the day, once 100 pesos and the second time it was 200 pesos because it was a few errands with many stops, he carried stuff for me as well, I didn't ask him but he insisted. The last day he just took me to the airport, I gave him a 10 USD bill as I was running out of pesos.
I haven't asked a local about this specific situation at the time, but I know locals do tip drivers/waiters and I did that in my previous visits. I think my estimation was right because the guy seemed happy and helpful. You might not be obliged to do so, but it's always a good idea to help people on minimum wages.