Yes, a basic 'buck/boost' transformer doesn't take 120/208V (two legs from a 3 phase 208/120V system) and convert it into a 120/240V 'split phase' output. It provides 240V but the L-N voltages are uneven.
If you really need 120/240V, then you need a full 'isolation transformer'. (Well, there are some non-standard autotranformer approaches, but let's ignore anything that you can't order out of a catalog

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So -> check with the equipment manufacturer. Find out if your system really needs 120/240V split phase.
1) If it doesn't really need split phase, and doesn't really use the neutral, then you can use your existing transformer. See if you can disconnect the neutral so that it doesn't accidentally cause a problem.
2) If it does really need split phase, but you can limit the 120V load to only one leg, and you are willing to take the risk that a mis-connection will put 140V on that leg, then you can carefully insure that the 120V load is on the 120V leg.
3) If it does really need split phase and you want to provide true 120/240V split phase, then you need a different transformer.
-Jonathan