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I think the dot product just projects onto the measurement basis. For standard basis, phi is a one-hot vector and the dot product just selects an entry of psi. The entry times its complex conjugate is the probability of measuring phi, as opposed to a different one-hot vector.
There is no probability of measuring phi.. only its eigenvalue
Every different technical field invents different nomenclature for what are essentially the same concepts. 'Non-standard terminology' assumes a preferred frame of reference! :D Brb, googling 'one-hot'.
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