Although, mirrorless are getting much better, even using the site you reference, DSLR's are still faster (Except for some of the oldest models) than mirrorless in terms of shutter response. Startup time is not a very significant issue, unless you happen to swim around with your camera turned off.
In terms of time taken to get the shot, autofocus speed is just as important, if not more important, than shutter lag, as it is really these two intervals together that are important. Autofocus speed is of course dependent on many things, type of autofocus mechanism, lens, amount of change in focus distance measured etc. The Panasonic cameras do seem to be the fastest mirrorless cameras taking both shutter lag and autofocus into consideration, at least from what I read.
Ultimately it will now come down to individual experience using the camera, as well as their needs; with modern dslr's using in lens autofocus generally still being the fastest. On land, the acid test is still sports photography, underwater the speed requirements are generally less.
There are situations such as shooting sharks, dolphins, and of course topside breaching, where having the fastest possible camera can make all the difference.