Can't comment on BTw performance tester and Firefox combination with FTTP, however, there certainly were well known and well documented issues with this combination on VDSL/FTTC service, an alternate browser to FF was always recommended with the BTw checker.
In general, the BTw performance tester is very poorly rated for accuracy, certainly on ADSL/VDSL service, on my line US data speed is consistantly reported as higher than synch speed!
I always use Speedtest.net now which produces much more consistant and believable results with any browser I have tried.
I'am sure some of the many FTTP service forum patrons will offer more applicable observation.