The bonus disciplines are in addition to the number shown on Mystic class feature table.
So an awakened mystic would know 2 + N disciplines, where N is the number of disciplines shown on the class level table.
Specific beats general.
From the Player’s Handbook:
If a specific rule contradicts a general rule, the specific rule wins.
The class table gives general rules for the mystics, and the subclasses give features specific to particular subclasses. Bonus Disciplines is an exception to the general rule for disciplines known.
The bonus disciplines feature says:
At 1st level, you learn two additional psionic disciplines of your choice.
Specifically, the Awakened mystic knows two more disciplines than mystics generally know.
The alternative erases the class feature by 5th level.
If it is the case, as your friend has stated, that you only have extra until the table catches up, then by 5th level this class feature, Bonis Disciplines, is gone; and not only gone, just flat contradicted - it says you have additional, except you don’t?
We can think about this by comparing it to the Order of the Soul Knife. Notably, the Soul Knife does not receive bonus disciplines.
Does the following situation make sense?
5th level Awakened Mystic knows 3 disciplines, and has a feature that says they learn two additional disciplines.
5th level Soul Knife Mystic knows 3 disciplines and does not have a feature that lets them learn two additional disciplines.
Of course this is obviously not intended. The awakened mystic would quite literally lose a class feature, but the soul knife mystic keeps theirs.
It would also be a technical nerf to the subclass when compared to the Soul Knife. Notably, the bonus disciplines feature are order restricted - they can only be taken from a particular order. If in the end the awakened and the soul knife have the same number of disciplines, the soul knife will have greater flexibility - they can take all their disciplines from any order. The awakened has two of their disciplines order restricted, a nerf to flexibility.