OP
All UPS systems (used in broadcast) are linked together (control wise) so that the Red, Yellow and Blue phases between UPS's remain in sync. You are correct that the outgoing phase maybe be different (not much) from the incoming because of the conversion from ac to dc and back to ac. But when connecting the outputs of each UPS to a dual mains MDU (mains distribution unit) the phases must be in sync, because the MDU's will switch at the zero crossing of the current cycle to minimise spikes and surges. The use of dual mains i/p MDU's are used mainly for euipment that have only have a single PSU.If you are using a double conversion UPS i.e. ac to dc to ac
The voltage between any outgoing cable of 1 UPS could be 400v different from an outgoing cable of a second UPS
As a general rule, neither UPS will sync it’s outgoing frequency to either incoming mains or a secondary UPS
Therefore, frequency difference (very small) will likely shift the phase angle between the 2 UPS units outputs.
There are some special circumstances where the above will not apply.