Such a person spares no expense when it comes to luxuries yet refuses to part with even a penny when someone else's needs (especially of those who are poor) are concerned?
In spite of being a millionaire, he is [a] [noun or adjective].
"1.1 Having or showing an intense and selfish desire for wealth or power."OLD
"2: marked by greed : having or showing a selfish desire for wealth and possessions"MW
For completeness, definition for selfish:
"If you say that someone is selfish, you mean that he or she cares only about himself or herself, and not about other people."CD
‘Therefore many greedy landlords do not do repairs, unless forced to.’1
‘In fact our rulers are greedy for even more to go into their pockets at our expense.’1
‘Thus, banks became greedy, taking on huge risks in hopes of even bigger rewards.’1
In spite of being a millionaire, he is greedy.
Or a bit more poetically:
In spite of being a millionaire, he is driven by greed.
Driven by greed mentioned by Collins Dictionary