If you are using the pellets and the applicator gun you should be fine afterwards as the water from the hose is helping it get down into the soil where it can get to work but it probably wouldn't hurt to do it right before you plan to water the lawn either.
If you are using the liquid TR and spraying it on the lawn you will want to water it in immediately after applying it as it needs to be in the soil to work which is why I think the hose end sprayer is the way to go with TR and it's cheaper too.
Might be a dumb question but is there a way the pellets could be crushed and be dissolved and used in a spreadermate?
Not really a dumb question as it is "possible", I just don't know what the dilution rate would be. I know the Tournament Ready pellets are suppose to cover 16,000 sq/ft and they are 8oz pellets so I guess you could extrapolate from there. I will say that I have been using the H2O Maximizer Pellets and have been melting them down in a gallon of water and adding them to my EZFLO just to help a little, not sure how much it helps but I'm sure it helps the irrigation water to be a little more efficient.
The pellets are basically a solid form of the liquid so it's basically a bar of soap and I have been able to dilute a pellet in 1 gallon of water, the hotter the better as it will melt easier and faster. I will also say that after you have handled some wetting agent, you can definitely tell a difference between it and baby shampoo, it has a lot more staying power and it creates a film on whatever it touches, especially when it's concentrated.