Thanks Ravi. The sequence check for 100000000 was a good tip - though I checked, my settings are in sync.
My understanding is, once fields are mapped (either auto by system, or manually by matching to like fields across entities), the data can then be fetched by a process to populate even a non matching field such as text. This function however seems to be inconsistent.
In the above case, while re-checking, I realised a wrong mapping, which when corrected, is populating data automatically even without a process ! Perhaps something fundamental I have incorrectly understood on mapping and fetching (lookup) of data ?
Example:
A contact is pegged as primary or secondary in Account. Against Account, invoices are raised. I want to fetch salutation of customer in Account (and then later in invoice). Even through the relationship is maintained, the auto populate does not happen, and process led populating returns blank. (I hope you don't mind I will share this setup instead, for your shedding some light?)
Relationship mapped : 1: N Contact to Account (Referential), Salutation manually mapped.

In account_primary_Contact, there are no mappings (only system).
For secondary contact (new_contact_account_SecondaryContact), the manual mapping of two optionset fields is :

... and then published. Since primary does not show mapping option, not much I can do there - i assume system can show.
Now when i tag two contacts in account against primary and secondary, the mapped fields do not automatically populate the data. So created a process as :


The 'Title Primary' and 'Title Secondary' are simple text fields, as process does not allow reference update in optionset / lookup fields (or does it?!)
Now the process run just does not pick up the values for title in account.
I am imposing a long thread on you - grateful if you can guide. Have spent zillion hours now in trying to address this one last bit of mystery left before taking go live. Huge thanks !