Swallowing the slight moisture that remains in the mouth after rinsing during ablution does not break the fast. It is sufficient to spit out the water after rinsing the mouth. The small amount of moisture that may remain has no legal significance (sharʿī importance) regarding the validity of the fast.
However, as a matter of ḥiyṭah (precaution), it is recommended (mustaḥabb) — though not obligatory — to spit once more after rinsing.