jantoramuShya janane vidhishambhudR^iShTau 
	rAgAdineva rajasA tamasA cha yoga: |
dvaipAyanaprabhR^itayastvadavekshitAnAm
	sattvam vimuktiniyatam bhavatIyushanti ||

Meaning:

O Deepa Prakasha!
amuShya 			- This 
janto: 				- creature 
janane 				- when born, 
vidhi shambhu dR^iShTau 	- if it is seen by Brahma and Shiva, 
yoga: 				- it gets associated, 
rAgAdinA iva 			- like a dye with clothes, 
rajasA 				- with rajas qualities 
tamasA cha 			- and tamas qualities. 
tvad avekshitAnAm 		- Those seen by You 
bhavati 			- attain 
satvam 				- sattva qualities 
vimukti niyatam 		- which assuredly will get them moksha. 
iti 				- Thus 
ushanti 			- say
dvaipAyana prabhR^itaya 	- maharishis such as Vyasa.

Vyakhyana Saram:
The three qualities rajas, tamas and sattva are associated with Brahma, Rudra and Narayana. It is said that a jiva, if seen by one of these deities as he is born, will have the corresponding quality in him ("pashyatyenam jAyamAnam brahmA rudrota vA puna: | rajasA tamasA chAsya mAnasa samapiplutam ||").

Swami Desikan is saying that if Brahma or Rudra see the jiva, then just as the color of a dye will stick to a cloth, so too the quality of rajas or tamas will stick to the jiva.

As stated in Mahabharatam
jAyamAnam hi puruSham yam pashyen madhusUdana: |
sAtvikas sa tu vinjeyas sa vai mokshArthachintaka: ||
whoever Sriman Narayana sees as they are born will have sAtvika qualities in them and will seek moksha. This is said by great maharishis such as Vyasa.

This is echoed by Azhvars in verses such as "anRu karuvarangaththuL kidandhu kai thozhudhEn kaNdEn" and "madhiL thiruvarangam ennA karuvilE thiruvilAdhIr".