How are antenna arrays synchronized for direction finding/localisation?
Absolutely, that delay difference has to be compensated for in some way. This is usually done by matching the feed line lengths to all of the antennas so they are identical to within some precision. Depending on what the antennas are connected to, it may also be possible to compensate for the delay somewhere else.

As far as time synchronisation of separate receivers, this is usually done by locking them on to some sort of common time and frequency reference signal, such as GPS or perhaps a higher resolution frequency standard transfer system.