All these examples seem to be...different. I cannot make sense of it.
Il a déjà tant fait.
Il travaille tant !
J'ai dû partir, tant j'étais fatigué.
Yes, the placement of tant is weird. A good dictionary will explain the rules. Mostly. The adverb tant has a slightly dated feel, which may be a cause or a consequence of its placement partly obeying rules of old French.
Normally tant comes after the verb, which is the default place for an adverb.
Il travaille tant !
Il travaille tellement !
Il travaille beaucoup.
With a compound tense, tant usually goes between the auxiliary and the verb.
Il a déjà tant fait.
Il en a déjà fait tellement.
Tant can also act as a subordinating conjunction. In that case, it is naturally placed at the beginning of the clause.
J'ai dû partir, tant j'étais fatigué.
J'étais si fatigué que j'ai dû partir.
J'étais tellement fatigué que j'ai dû partir.