Lawn care in Manatee county (2014, mover, home)

[ctwhitechin]

Quick question for any green thumbs out there. We moved here in 2014, had a home built, and it is my first experience caring for a Floratam st. Augustine lawn. Well long story short, I burnt part of it with too much fertilizer. So, since $ is tight I bought about 10 trays of sod plugs and planted them , before I did I put a scoop of good compost in each hole I dug, everything I plant in the stuff has done super so far.

Anyway I planted the plugs on Saturday and Sunday, already I see I think they are called stolons branching out from the plugs in every direction above ground. Bought them from a store called the big earth, salesperson told me no need to strip grass down to bear soil, the plugs will spread out and grow over the burnt areas and eventually connect.

Does that sound right? I kid you not, after 5 days some of the plugs are touching each other via these grass "runners" but I don't understand the logistics of it all, do the runners then establish new roots? I mean if I use the lawn mover I imagine I would just separate the plugs apart again...I never worked with grass that grew sideways before. Any help would be greatly appreciated, the compost I used is like superfood I guess for plants, everything i put in it sprouts right up.

How long do these plugs take to grow some roots, about a month? Thanks for any advice, all I want is a green lawn again.