According to interpretations on the Bona Need Rule (see B-202222, DECEMBER 31, 1981, 61 COMP.GEN. 184) that modifications to a severable service contract providing for increased services must be charged to the fiscal year or years in which the services are rendered, so the change would need to be funded with current funds at that time. Your "Question Background" indicates that in the second FY of the contract funded with prior year funds, that the requirement is being increased - this would be a bona fide need to the year in which the change is made.
However, for modifications within the general scope of the original contract, the situation is a bit more complicated. Most government contracts contain provisions which, under certain conditions, render the government liable to make equitable adjustments in the contract price. Such liability may arise due to changes in specifications, government-caused delay, changed conditions, increased overhead rates, etc. These conditions are set out in standard contract clauses such as the "Changes" clause, "Government Property" clause, or "Negotiated Overhead Rates" clause.
Therefore, it is truly new scope, the bona fide need is in the year of awarding that modification. If it is within the current scope and the contract just incurs a cost/price increase, the bona fide need would tie back to the original award and could be funded with the prior year money (using your example). There clearly need to be a determination of what type of modification your situation falls into to make a more definitive determination of your situation. It is also recommended that you consult with a Fiscal Law attorney within your organization to get an official read on this.