Thumma is a conjunction marking sequence, often with an intervening interval. Yaʾtī is an imperfect verb from ʾ-t-y, 'to come'; its implicit subject is the pilgrim.
Makkata is an accusative place expression governed by this use of the verb. In min yawmihi, min is a preposition, yawm is the genitive idafah head, and -hi is its attached possessor. Al-ghad is tomorrow; baʿd al-ghad is the next day after it.