TL;DR: Infinitive suffix "-ти" and 3rd person singular present "-тъ" are essentially different.
They could reduce independently in Slavonic languages, but if they are both reduced, this seems to be just a coincidence.
In his "Slavonic Grammar with Correct Syntax" (1619), Meletius Smotrytsky marks 3rd person singular present suffix -тъ
(pronounced with short [ɔ]
).
So, the verb to read, "читати" [t͡ɕɨ-ta-ti]
conjugates to "чтєтъ" [t͡ɕtɛ-tɔ]
.
Here's the scan of Smotrytsky's work

Links: exact page, title page.
In modern Slavonic languages, indeed, these suffixed often reduce.
Ukrainian (my native language): the infinitive suffix remains the same, while the 3rd person singular present suffix reduces: "читати" [t͡ɕɨ-ta-tɨ]
→ "читає" [t͡ɕɨ-ta-ʲe]
or even "чита" [t͡ɕɨ-ta]
in Western dialects.
On the contrary, the modern Russian reduced suffix in the infinitive form while it retains 3rd person singular present suffix: "читать" [t͡ɕi-tatʲ]
→ "читает" [t͡ɕi-ta-ʲet]
.
So, as we can see, the distinction between Ukrainian and Russian suggests that both suffixes may retract independently.