One should consult one's Guru to decide whether to use dwitArI [hrIm shrIm] or tritArI [aiM hrIM shrIM] or chatuH tArI [OM aiM hrIM shrIM]. It would depend on which Tantra is used as pramANa – vAmakeshwara, Kalpasutra or paramAnanda, Vamakeshwara agreed as the oldest in this list even by the likes of Bhaskararaya. As Rudrayamala points out, ChatuH tArI should be used based on one's Varna [shUdrAdi yavanAntAnAm tritAri parikalpanam etc]. The details of the use of praNava as applied to the scheme of four Varnas are discussed by Sri Bhaskararaya in the beginning of Saubhagya Bhaskara.
As far as Rashmimala is concerned, people add tritAri or chatuH tAri or whatever they like, because of a blind interpretation of the sUtra – sarveShaaM mantraaNaamaadau tritArI samyogaH. Some go to the extent of even adding Tritari or ChatuH tari to the Mula Mantra during Japa. This is contradictory to the purport of the Sutras. Sri Bhaskararaya clearly points out:
Yagamandirapraveshottarameva asya pAThaH tataH prAkkR^ityamantreShu na tadyoga Avashyaka iti |
Only rites prescribed after entering the pujA mandira need the tritArI prefix and not others. So, Rashmimala Avartana, which is done as a part prAtaH krtya, does not need the addition of tritArI, chatuH tArI or whatever. One may ask if tritArI or chatuH tArI can be added during Japa of the mUla mantra. The answer would be a clear `no' again.
asyA shaktipUjA mAtre viniyogAt puMdevatApujAyAM strIdevatyA nyAsajapAdau vA na viniyogaH |
The addition of Dwitari, Tritari of ChatuH tari is limited for Shakti Puja. Adding the same for pUjA of male deities like prAsAda sambhu or mahAgaNapati [exception would be when the AvaraNas for these deities is performed as an anga to Srikrama] or using the same for Nyasa or Japa of even Srikrama Devatas is not prescribed. When there are different pramANas on the same topic, sampradAya is the pramaANa which guides which of the several but valid pramANas need to be accepted. However, one cannot follow something in the name of sampradAya when shAstra pramANa is violated thereby.
vande guruM shankaram