What is the ruling on thanking a benefactor with the phrase "To God belongs your excellence, and upon Him be your thanks"? And does "upon Him be your thanks" mean compelling God to give thanks? And is "upon him" used to mean "from him"?

The common phrase "Lillahi Durruk wa 'ala Allahi Ajruk" (May Allah bless you and may your reward be upon Allah) is correct and has no issues. This is because the expression "'ala Allahi Ajruk" (your reward is upon Allah) is found in the texts of revelation, such as His (the Almighty's) saying: ﴿فَمَنْ عَفَا وَأَصْلَحَ فَأَجْرُهُ عَلَى اللَّهِ﴾ (But whoever pardons and makes reconciliation - his reward is [due] from Allah), and His saying: ﴿وَمَنْ يَخْرُجْ مِنْ بَيْتِهِ مُهَاجِرًا إِلَى اللَّهِ وَرَسُولِهِ ثُمَّ يُدْرِكْهُ الْمَوْتُ فَقَدْ وَقَعَ أَجْرُهُ عَلَى اللَّهِ﴾ (And whoever leaves his home as an emigrant to Allah and His Messenger and then death overtakes him - his reward has already fallen upon Allah). This means that Allah the Almighty has guaranteed the reward for righteous deeds out of His grace and generosity, not as an obligation upon Him due to the servants' deservingness.

Likewise, the expression "'ala Allahi Shukruk" (your gratitude is upon Allah) has the same meaning as "'ala Allahi Ajruk," as in the hadith of the man who gave water to a dog, and Allah appreciated him and admitted him into Paradise. The word "'ala" here can linguistically mean "from," as in His (the Almighty's) saying: ﴿الَّذِينَ إِذَا اكْتَالُوا عَلَى النَّاسِ يَسْتَوْفُونَ﴾ (Those who, when they take a measure from the people, take in full). The main intent of these phrases is usually supplication.