[talanum1 (OP)]

The parallel Worlds of Quantum Mechanics come into existence on observation. I observe continuously, therefore do parallel Worlds start existing continuously i.e. does infinitely many parallel Worlds start existing in any finite time?

[Halc]

The parallel Worlds of Quantum Mechanics come into existence on observation.

No.

Everett does NOT postulate [that] at certain magic instances, the the world undergoes some sort of metaphysical “split” into two branches that subsequently never interact.
...
According to the MWI, there is, was and always will be only one wavefunction, and only decoherence calculations, not postulates, can tell us when it is a good approximation to treat two terms as non-interacting.

This means no worlds 'coming into existence' despite the visual made popular by DeWitt who coined 'MWI' for the interpretation. Such a metphysical split would violate Everett's one and only postulate, that "All isolated systems evolve according to the Schrodinger equation".

Secondly, in any but a very few implausible QM interpretations, observation plays no role. In other words, humans, consciousness, etc play no role. Interaction of one system with another, disrupting coherence of one system otherwise in superposition is what matters.