Do I need to associate an asset with an expense if it's paid in full?

I don't understand what you are asking

if you buy an asset, that is not an expense at all, it is a purchase of something you keep on the books as an asset or as inventory.

If you bought an asset and borrowed money to do so, the full amount borrowed is the cost of the asset, and the debt is now a liability account, you pay down the loan.  That is also not an expense, and when paid down does not affect the asset cost

Could you explain in more detail please?

A computer system was purchased by an employee and the purchase was reimbursed through payroll and came into Quickbooks as a journal entry that attributes it to a reimbursement expense. It's over $2500, so it should be added as a fixed asset, correct? And if it's added as a fixed asset, what about the reimbursement expense? Another complication is that the reimbursement journal entry includes other reimbursements and would need to be split out if it needs to be associated with something else.

A computer system was purchased by an employee and the purchase was reimbursed through payroll and came into Quickbooks as a journal entry that attributes it to a reimbursement expense. It's over $2500, so it should be added as a fixed asset, correct? And if it's added as a fixed asset, what about the reimbursement expense? Another complication is that the reimbursement journal entry includes other reimbursements and would need to be split out if it needs to be associated with something else.