What "firstfruits" means
The name is not a metaphor we invented for an app. It is an old agricultural practice, and the shape of it is the whole idea: the first part is given, and the rest is yours to enjoy without guilt.
The practice
In the law given to Israel, the first of the harvest - not the leftovers, not whatever was still there at the end - was brought and offered before any of it was eaten.
"You shall bring the first of the first fruits of your ground into the house of Yahweh your God." Exodus 23:19, World English Bible (public domain)
"Honor Yahweh with your substance, with the first fruits of all your increase; so your barns will be filled with plenty, and your vats will overflow with new wine." Proverbs 3:9-10, World English Bible
Two things are worth noticing. First, it is about order, not amount: the offering is small, and its significance is that it comes before everything else. Second, the rest is not confiscated. The barns fill; the vats overflow. Firstfruits is not a vow of poverty, and it is not a vow of silence about your phone.
Why that shape fits attention
Most of us do not decide how to spend our attention. It is taken, in small amounts, by things engineered to take it, and what is left over at the end of the day is what God gets - if anything is left. The firstfruits pattern inverts the order without demanding the whole harvest.
That is why the app is an exchange rather than a schedule or a lock. You are not being punished for having a phone. You are being asked to give the first part of your attention, and then the rest of the day is genuinely yours - which is why the emergency exit is in plain sight and costs nothing.
The word in the New Testament
The image keeps going. Paul uses it for the resurrection - Christ as the firstfruits of those who have fallen asleep (1 Corinthians 15:20) - and for the Spirit as a first installment of what is coming (Romans 8:23). The first part is not the whole thing; it is the sign that the whole thing is on its way.
A caution about the app
Five minutes in the morning is not obedience, and a streak counter is not devotion. An app can shape a rhythm; it cannot do the thing the rhythm is for. If Firstfruits ever becomes a score you are protecting rather than a door you walk through, delete it - it has no account, so there is nothing to lose by leaving.
Scripture quotations are from the World English Bible, which is in the public domain. Firstfruits the app contains no Bible text of its own - it counts the time you spend in whichever Bible app you already use. How that works.