It was not stated that the 'Mac Mini' was purchased with 'Tiger', MacOS X 10.4.x' installed; but 'came' with it; thus ...
... if the 'Mac Mini' is of of the original PowerPC series - it supports MacOS X 10.3.7 and later. The 'Mac Mini (Late 2005)' [2nd generation 'Mac Mini's] series came with MacOS X 10.4.2 [but, may be 'Panther', MacOS X 10.3.x, capable - see (1) below]. The Intel based Mac Mini's [3rd generation 'Mac Mini's] require MacOS X 10.4.5 and later.
With respect to attempting to install 'Panther' from a PowerMac / iMac G5 installation disc - nice try, no prize.
'Are the install discs architecture dependant????' - exactly, yes.
'if so does anyone know of a workaround??' - purchase a 'retail' (full install) copy of 'Panther'.
Borrow the 'retail' installation discs to perform (1) below, if you successfully install and boot from 'Panther', then purchase a 'retail' copy for possible re-installations (the 'new' MacOS way of solving software / OS related problems).
(1) - To see if the 'Mac Mini (Late 2005)' series can boot with 'Panther', MacOS X 10.3.x' - install 'Panther' onto an external FireWire hard disk drive, hdd, and attempt to boot from the external FireWire hdd.