Where do you live?

Letting someone help you while you're gone on vaca used to be one of the top 3 issues on this forum. I used to tell people to weld their mower at the highest setting, because there really is never a good reason to lower it for St Augustine. Raise your mower back to the highest setting and mow when the grass gets up to around 5 inches high.

Without knowing where you live or what your sprinkler output is, I will say that in general 1 hour per week is not enough. I live 40 miles nw of San Antonio in the Texas Hill Country and am allowed to water 5 hours every Tuesday. With oscillator sprinklers that is barely enough this time of year. If you live in the humid south (Houston to Orlandoish) you can get away with either less time or longer duration between watering. Here's more on watering...

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Rye grass? Never. People do it, but they should not. I'm not just saying this because I don't like rye. If you have rye in the winter, the rye grass will delay the return of the St Augustine in the spring. You end up with more weeds than you would have had the St Aug kicked off in March. That means more chemicals and St Aug is a little sensitive to chems, so just leave the rye on the shelf.