What would happen if 2.4 Volts is applied, instead of 1.25 Volts, to an FPGA?
IF the random reconfigurations and running warm happen with 2.4 Volts applied rather than 1.25V applied you MAY have been lucky.

If the above results occur when 1.25V is applied then they HAVE been "smoked". They are walking wounded and you have no certainty that they will not die or behave in any possible way whatsoever in future. If these are for anything other than non critical in house use by competent technical people they should not be used. For personal in house use by competent people you can assess the value of the time wasted against their replacement cost. 

Note that they MAY appear to work perfectly in ,any cases but do bad things occasionally. 

Why did they not die? They did by any reasonable definition. 
 example only:   pedestrian hit by a car will die about V^2/50 % of the time, V in kph. ie at 70 kph death is near certain. At 50 kph death occurs about 50% of the time. Above 70 kph SOME people will survive but its a fluke. At 40 kph almost 40% fewer people will die than when hit at 50 kph so even modest braking helps a lot.
 Overvolatged FPGA's are obviously vastly different than this but will also have a death / voltage relationship. 

Long long long ago (30+ years?) I (stupidly) transiently applied about 50 VDC to a complex multi IC assembly with several separate PCs in it. Circumstances meant I had to repair it. Replacement was not an option. Most ICs were socketed (thankfully). I found that most higher current capable driver type ICs had died and that about none of the glue logic ICs had died. An interesting lesson. I haven't managed to do anything quite so major since. 



NB !!!

TESTING !!!

You already know the following, but all of us often need to know it better :-).

A major "problem" here was lack of testing.
 Testing of a manufactured product needs to be carried out by somebody who has your interests paramount and not those of a supplier.

While you cannot test for everything, as this sort of problem could be caused by other types of faults (track short, via open, wrong resistor value, misinsertion, poor soldering, ...) and as the outcome is potentially fatal to the product, testing should detect such problems. 

You need to trade off testing cost and complexity against product cost and run size etc, but chances are that good testing here would have saved you money. 

Cost of faults can be far far more than component costs and remediation. Loss of customer business and reputation is often an issue and impact on end user profitability is likely.