I play a druid so Dots and Hots are important to me and Id love to see them in game, and I think your spot on the dot about time being the governing body of these rules and how they will fit in :)
I planned out some rules under my Illidan for WoW minis thread as my interpretation of how I'd do things like standing in AoE damage that ticks. For example Illidans Flamecrash - That left an AoE marker that would damage everyone on or adjacent to that hex, and placed 3 DOT markers at regular time intervals on the main clock (in this case placed at intervals of 2 ticks each), anyone in the AoE would roll damage against them when the game clock reached those time intervals.
As for a heal over time, it would come in Actionbar card form I'd guess, so when you cast it on someone, you tap the card and place it on their character card to show it in effect then similar to the above - place Hots markers at time intervals on the game clock to show when effects pop.
The catch with that though is if you have lots of effects going, it could become confusing with keeping track of whos Hot is that, whos DoT is that etc, and clutter up the Game Clock and bog down a fast playing game - hopefully there will be a nice clean and elegant way to compliment the Base10 system.
Having it pop everytime someone activates might be less cluttered, but doesnt give a regulated time effect - Hots and Dots are supposed to tick at a constant time, so if you swing with your massive axe it will take longer before your heal effect or damage effect kicks in.