An ATS responds to a LOSS of power and creation of power by a generator. So the "transfer time" of an ATS is, as Bill said, almost irrelevant when it comes to electronics. An ATS will not even BEGIN its process until AFTER the primary source has ALREADY failed. Then you have to wait for the generator to spin up and the voltage to stabilize. Only THEN will the ATS change over, by which time your electronics have long ago (in a relative sense) shut themselves down.
As mentioned, you need a UPS to carry you through that process. UPS come in two main "flavors"; "On-Line" and "Stand-by". On-line are always supplying the load via the inverters through the batteries, so there is no transfer time involved. Stand-by have a little transfer switch inside (often solid state) and can transfer in a matter of milliseconds to seconds, depending on how much you are willing to spend. You need to first define what your electronics can tolerate, then get a UPS system that is appropriate for the worst case scenario, with a battery pack long enough to carry you through the ATS based process.
" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden