I don't have the app version, so cannot comment on the discrepancy between the two versions.
To answer the question you raised in the original posting of "Which is correct?" the answer is most likely, neither.
Tinseth is based upon a model developed by Glenn Tinseth on the system he brewed with many years ago using dried hop cones. Depending upon the actual length of chilling as compared to the system Glenn used, your results will vary widely from his.
Rager follows a utilization curve which is just not normal for chemical reactions.
Neither modeled the utilization of whirlpool hop additions.
Even if the two pieces of software agreed, there would be only a slim chance if they gave the closest answer for your process.
To make matters even hazier, the calculation for IBU measures the amount of isomerized alpha acids at a wavelength where there is interference from other compounds in the hops which absorb at that frequency. Further, there are other compounds in the hops, such as the beta acids which can contribute to the sensation of bitterness when oxidized and are not measured using the spectrophotometric method for IBUs.
You have narrowed the issue down to the way the two pieces of software calculates a value of continued IBU contribution of boil hops in the whirlpool. Personally, I have that box unchecked as I know from experience what bitterness level I want to target for my process to get the bitterness sensation I aim to achieve. In essence, this is the key: Did you get the perception of bitterness that you wanted? Once you can understand this hedonistic experience correlation to the IBU numbers, then you know where to set the value to get the bitterness experience you want in your beers.