As I understand it, an MPPT algorithm adjusts the charging voltage
No, it doesn't. The MPPT algorithm in most set-ups changes the input impedance of a buck converter in such a way that the output current of the buck converter is maximised. This keeps a solar panel at its MPP.
The input of the buck converter is regulated, the output isn't, and the output will behave roughly like a current source; the output voltage is set by the battery, not by the MPPT algorithm, or the charger.
If the MPP is at 18 V, then that is the voltage on the solar panel side and it has nothing to do with the voltage on the battery side, which is set by the battery.
A charger will, of course, have to make sure that a battery isn't charged beyond its maximum voltage, or charged with too large a current, but that is separate from the MPPT algorithm.
It does mean, however, that the solar panel will sometimes be moved away from its MPP; it could be delivering too much current/power at its MPP for some stages of the charging algorithm, especially when the battery is (almost) fully charged.