At this point in the year, St Augustine is going to be dormant and not spread anymore. This is a good time to lay down some dried molasses and compost, to get the soil ready for the spring. When it warms up, your St Augustine will start spreading out. You can't really overdo it with molasses and compost, as long as you work it in and don't completely cover up the grass blades.
I had this same issue with my yard. Two years ago, I bought a house with a Bermudagrass yard full of bare spots, and several large oak trees that were blocking a lot of sun. The first year, I tried the commercial stuff and didn't get any results. Last year, I put out St Augusting sprigs and they survived, but didn't do much in the way of spreading out. This year, I trimmed out the trees at the end of winter to let more sunlight in, put down dried molasses and compost. The St Augustine really started to spread over the summer. I used fescue seeds in the large bare spots and they filled in nicely. Over the summer and into the early fall, that St Augustine is starting to move in and displace the fescue.