An Tuiseal Ginideach

As 'tar éis' is a preposition, you don't use the tuiseal ginideach for the word following it. The TG is only used when two nouns come together.

Tar éis consists of the preposition thar and the noun éis, so it puts the following noun in the genitive - tar éis an lae, tar éis a bháis, tar m’éis.
There are a lot of these ‘compound’ prepositions, (preposition + noun), in Irish and they all take the genitive.
Here are a few of them ar aghaidh; ar feadh; de bharr; faoi/fé choinne; in aice; i ndiaidh; le haghaidh; os cíon…
Some of these are often shortened in spoken Irish for example in Munster you will often hear fean/fan instead of ar feadh, héis for tar éis, nós for ar nós but still followed by the genitive.

Tar éis traditionally takes the genitive as "éis" is a noun originally meaning "trace" or "track".

However in the spoken Irish of Munster many speakers no longer place the following noun in the genitive.

Note in general that in modern spoken Irish, native speakers rarely place a noun in the genitive if it is followed by an adjective:

An cogadh
Deireadh an chogaidh

but:

An cogadh mór
Deireadh an chogadh m(h)ór (They may or may not follow the genitive lenition rules on adjectives)

An bhean
Ag pógadh na mná

but:

An bhean rua
Ag pógadh an bhean rua.

The Caighdeán of course prescribes use of the genitive in these cases, but spoken Irish has being dropping the genitive since the 1750s.