When a company reimburses you, it means you have paid money to do something and are given back a portion of that money at the end of the task. For example, you pay $1000 for a plane ticket and the company reimburses you $600, therefore you only pay $400 total for the ticket. The exchange of money happens twice here. You first paid $1000, then are returned $600.
When a company subsidizes you, it means they will cover the cost of something immediately, therefore making it cheaper. For example, the company will subsidize $200 for your plane ticket that costs $1000. Therefore you will only pay $800. The exchange of money happens once here. You pay $800 for the plane ticket because the company has made it cheaper by $200.
The example sentences you have provided work well. To understand the difference, think about how the money is being handled.