But that's present vs past tense, which is independent of the subjunctive mood. The indicative version of the first sentence would be "insisted that he spends." While placing the verb form into the past tense sounds odd to my American ears, the form "spent" could be either indicative or subjunctive. (The subjective is formed by using the plural form, which makes it indistinguishable in many cases, including the past tense of regular verbs.)
> But that's present vs past tense, which is independent of the subjunctive mood.
No, it's subjunctive vs. indicative.
The British form is indicative and past tense, which is not correct grammar under either British or American rules, but is used in common speech.
Replace the verb with "to be", e.g. "the doctor insisted he be here." vs. "The doctor insisted he were here." to illustrate that the past subjunctive doesn't fit.
The past subjunctive is almost exclusively used for hypotheticals, e.g. "If I were rich...."
This isn't hypothetical. This is a mandative statement, so we use the infinitive form of the verb even if the action took place in the past.