It is pertinent to note that although Rishi Agastya drank the ocean the earth was not devoid of water i.e. seas, rivers etc. were still around. This can be confirmed from Vana Parva.
After Devas had slain the Kalakeya demons, they asked Sage Agastya to replenish oceans but he replied
'That water in sooth hath been digested by me. Some other expedient, therefore, must be thought of by you, if ye desire to make endeavour to fill the ocean.'
The Devas along with Vishnu ji then approached Brahma ji who said
Go ye, O gods! whither your pleasure may lead you, or your desire conduct you. It will take a long course of time for the ocean to resume its wonted state; the occasion will be furnished by the agnates of the great king Bhagiratha.' Hearing the words of the (universal) grandfather (Brahma), all the foremost gods went their way biding the day (when the ocean was to be filled again).'
Then Vana Parva gives lineage of Bhagiratha. Emperor Sagara from Ikshvaku Dynasty had sixty thousand sons from princess of Vidarbha and a son Asamanjas from princess of Sivi. Ansuman was Asamanjas' son who and his son was Dilipa. Dilipa made great efforts towards the descent of Ganga but was unsuccessful. The task was completed by his son Bhagiratha .
Now there are at least two references to water bodies other than ocean in the time period between Sage Agastya drinking ocean water and Emperor Bhagiratha bringing about the descent of Ganga.
First one is when Sagara's sixty thousand sons failed in their quest to locate the horse meant for Ashwamedha yagna that disappeared in front of the waterless ocean. They mentioned to Sagara
'O Protector of men! O ruler of the earth! O king! by thy command, the whole of this world with its hills and its forest tracts, with its seas, and its woods, and its islands, with its rivulets and rivers and caves, hath been searched through by us. But we cannot find either the horse, or the thief who had stolen the same.'
Next reference is when describing the cruel nature of Asamanjas. It is said
he used to seize by throat the feeble children of the townsmen, and threw them while screaming into the river.
Based on the above references we can conclude that seas and rivers were still present even though oceans were devoid of water. And thus in this particular time period ocean life could be present in seas, rivers etc