We all have heard stories about why we celebrate Krishna Janmastami. I am here to just delve a bit into the diffrence in dates in celebrating Sri Jayanthi, Krishna Jayani, Gokulastami.
There are two main vaishnava temple agama methods. One is Vaikanasam. The other one is Pancharathram.
Vaikanasam: Brahma's son Vikanasar was born as a Munivar in the earth and he was worshipping Lord Narayana. To this Muni, Sriman Narayanan himself explained the sasthram (Rules) on temple-building, procedures of installation of idol for worship etc. Vikanasa Muni conveyed these sastras to his disciples Athri, Marisi, Kasyapar and others. Since Vikanasa Munivar was first to establish this agamam, it came to be called "Vaikanasa Agamam". This agama sasthram was brought into print form in the 3rd century A.D.
The principles under Vaikanasam are:
Lord Vishnu is Aadhi Purushan. From Him, evolved the other forms of the Lord viz., Sathyan, Achuthan, Aniruthan. Vakanasa temples will be normally built inside towns and not permitted to be constructed on hills. Also, Lakshmi is inseparable from Narayanan. She is the embodiment in five bhoothas, five states of Lord Vishnu (Para, vyuga, Vibhava, Andharyami and Archa). And, chit, Achit and Iswara are always sathyam. Worshipping can be done only to Lord Narayana with Lakshmi and to none other. So under Vaikanasa sastra, even Azhvars and Acharyans are not worshipped and so there won't be idols of Azhvar, Acharyars in temples. Even the tamil 4000 divya prabhandams are not recited in vaikanasa temples. Ahobhilam, Oppiliappan, Srivilliputhur temples are examples of Vaikanasa agamam. (Tirupathi, though installed on hill, is an exception for observing Vaikanasam)
Pancharathram: It is connected with the purusha sukhtham found in Rig Veda. At several places in Mahabharatham, Vasudevan is extoled as principal Lord as per Pancharathra agama principal. Originally, worshipping was through conducting Yagas and Yagnas. Only Pancharathra Agama set forth ways for building temples for worhip by installing vigrahas, conducting uthsavas and arranging veedhi ula of the deity. Pancharathra agama is appreciated in Mahabharatham, Srimad Bhagavatham, Vishnupuranam, Padhma puranam,Garuda puranam, Naratheeyam and Varaga Puranam. There are 108 samhithais in Pancharathram.
There are quite different schools of thought for fixing the name Panchrathram. One explanation is that originally this sasthram was followed in five paruvas of the year and five specific rathris were selected for the culminating the rituals. By another explanation, Ananthan, Garudan, Viswakshwnar, Kapali and Brahma got the upadeasam directly from Lord Narayana in five days.
Under Pancharathram, temples are constructed away from towns, on hills and on river banks. There is no caste difference observed under Pancharathram, All who get dheekshai are equal. Andal is worshipped equal to Lakshmi. Azhwars are also installed in temples and worshipped. The same five states of Sriman Narayanan are worshipped in Pancharathram as in Vaikansam. Srirangam, Kanchi, Melakkottai, Tiruvallur etc are pancharathra temples.
Now regarding Sri Jayanthi. Smarthas observe only ashtami thithi in Sravana month. Vaishnavas observe Ashtami merging with Rohini star in pathrabha month (next to sravana month). Here again, in temples, vaikanasas observe the evening - night time for the thithi and star combination. Pancharathra temples observe the combination at day time.
In the case of Munithraya anushtanam, which is common for Ashramam and Madam, the choice of the combination of thithi and nakshthra with timing of the day is decided by individual Acharyan. And, the sishyas have to blindly follow the instructions of their individual Acharyas.