Yes, that sentence would seem to mean that cities and civilizations still arise in Egypt today every time the river run offs at high tide—a state of affairs that couldn’t be possibly true. The semantic problem in that sentence is due to the wrong use of the temporal subordinating conjunction “whenever” as well as the wrong use of the simple past-tense “sprang” in the main clause and of the present-tense “overflows and scatters” in the subordinate clause.
For that complex sentence to yield the correct sense, the sequence of tenses in the two clauses should be corrected as follows:
“But through the Nile, cities and civilizations had sprung in places where the river would overflow and scatter fertile soil onto its banks.”
“Had sprung” is, of course, used here to indicate certain events in the indefinite past, and “would overflow and scatter” is used to indicate that the two indicated actions repeatedly (seasonally) happened in the past.