Earlier quoted context omitted.
The Ricci calculus has influenced Einstein only more than a decade later, in the development of the General Relativity (1917), for which tensor calculus was indispensable. It had no influence on the theory of Special Relativity (1905). Einstein is the one who changed the meaning of the word "tensor" to the meaning used today in most cases, when tensor means a general multi-dimensional quantity. I could not find any i…
He didn't specify general vs. special but there were lots of developments leading to special relativity too: https://en.m.wikipedia.org/wiki/History_of_special_relativit...
When the General Relativity was developed in 1917, the Ricci calculus was no longer recent, but it was 17 years old.
Therefore what the OP supposed, that there was an immediate causal relationship between these lines of work, is not true.