A past tense in the main clause (principal clause) is usually followed by a past tense in the subordinate clause.

He said that he wanted money. (NOT He said that he wants money.)
She replied that she was feeling better. (NOT She replied that she is feeling better.)
He replied that he would come. (NOT He replied that he will come.)
They climbed higher so that they might get a better view. (NOT They climbed higher so that they may get a better view.)

There are some exceptions to this rule.

A past tense in the principal clause may be followed by a present tense in the subordinate clause when the subordinate clause expresses a universal truth.

Galileo always maintained that the earth revolves around the sun.
Euclid proved that the three angles of a triangle are equal to two right angles.
The teacher said that honesty is the best policy.

When the subordinate clause is introduced by than, it can be followed by any tense.

I then saw him oftener than I see him now.
He liked your company more than he likes mine.

A present or future tense in the principal clause may be followed by any tense in the subordinate clause.