Pfthb

The following very MWE shows the issue, which disappears when the call to hyperref is commented:

documentclassarticle

defntextuptiny N
defttextuptiny T

usepackagehyperref

begindocument

$_t$
$_t$
$_t$
$_t$

enddocument

However, it compiles fine when hyperref is called before the two def.

If you use newcommand instead of def, you'll clearly see the source of the problem:

! LaTeX Error: Command t already defined.
 Or name end... illegal, see p.192 of the manual.

The t command is defined in the LaTeX Internal Character Representation for the “tie accent” and hyperref assumes this is the meaning of t. Since it has to do several patches for its working, you end up with t being essentially redefined to its original meaning, which can be seen if you add showt after begindocument

> t=macro:
->PD1-cmd t PD1t .

Without your redefinition and without hyperref, you'd get

> t=macro:
->OML-cmd t OMLt .

which is essentially the same (the encoding name may change when show is used for technical reasons which are beyond the scope of this answer).

Moral: don't use def if you don't know precisely what you're doing. And never redefine a command with renewcommand if you don't know precisely about it.