"The pillar of cloud did not depart" (Exodus 13:22). The verse tells us that while the pillar of cloud was still present, the pillar of fire was already growing forth.
The Cloud Stays Until the Fire of the Pillar Rises
Yalkut Shimoni on Torah 230:1
(שמות יג כב) לֹא יָמִישׁ עַמּוּד הֶעָנָן, מַגִּיד הַכָּתוּב שֶׁעֲדַיִן עַמּוּד הֶעָנָן קַיָּים הָיָה עַמּוּד הָאֵשׁ צוֹמֵחַ.