The suttas say about false speech:
He speaks falsehood. If he is summoned to a council, to an assembly, to his relatives’ presence, to his guild, or to the court, and questioned as a witness thus: ‘So, good man, tell what you know,’ then, not knowing, he says, ‘I know,’ or knowing, he says, ‘I do not know’; not seeing, he says, ‘I see,’ or seeing, he says, ‘I do not see.’ Thus he consciously speaks falsehood for his own ends, or for another’s ends, or for some trifling worldly end.
AN 10.211
In the Aṅgulimāla Sutta, the Buddha performed a feat of psychic power:
Then the Lord performed such a wonder of psychic power that the robber Aṅgulimāla, although walking with all his strength, was not able to catch up with the Lord who was walking at an ordinary pace.
Similarly, there is a story, somewhere, about a lady who was romantically in love with the Buddha therefore the Buddha performed a feat of psychic power causing his physical appearance to gradually age, which resulted in the lust of the lady dissolving.
A Mahayana webpage says:
In the Universal Gate Chapter, Bodhisattva Guanyin (Bodhisattva Avalokitesvara, in Sanskrit) transformed into different manifestations in accordance with different causes and conditions. Bodhisattva Guanyin has 33 different kinds of manifestations, including taking the form of sacred entities, devas, humans, the fourfold assembly, women, young boys and girls, the eightfold assembly, and vajrapani deities. Bodhisattva Guanyin transforms into various kinds of manifestations, using skillful means to attune to different sentient beings' temperaments and needs.
Why does Bodhisattva Guanyin often manifest into a female form, if he has a myriad amount of manifestations?
In conclusion, the Buddha performing physical impersonations with psychic powers is not related to false speech because the impersonation is a physical & mental action and not a verbal action. The same applies to Bodhisattva who manifest various forms for the sake of saving sentient beings from from wrong views that lead to hell or animal birth.