Apparently, Marx didn't think it is necessary to explain the implication of the word "tendency" except than emphasizing the gradual process numerous times:
"This gradual change in the composition of capital... then the gradual growth of constant capital... lead to a gradual fall… ever-increasing quantity of means of production through a constantly decreasing quantity of labour… each particular lot of commodities in the total mass of products, absorbs less living labour… Alongside the development of productivity there develops a higher composition of capital, i.e., the relative decrease of the ratio of variable to constant capital… The increase in labour productivity consists precisely in that the share of living labour is reduced while that of past labour is increased, but in such a way that the total quantity of labour incorporated in that commodity declines; in such a way, therefore, that living labour decreases more than past labour increases… therefore the absolute mass of the profit produced by it, can, consequently, increase, and increase progressively, in spite of the PROGRASSIVELY drop in the rate of profit. etc. etc."
The law of the tendency of the rate of profit to fall, is not a negligible, non-inherent, phenomena of capitalist production. It is the "logical necessity" of the DEVELOPMENT of capitalist production. It is how the development of capitalist production (i.e. growth of constant capital relatively to variable capital, growth of productivity of labor) works. I suggest Jim Miller's article: