Yes, you have the right idea. However, this is actually the direct imperative form, not the subjunctive. With direct imperatives used with an object infix, the infix becomes a prefix and the final -a changes to -e, as you see here. Although this form is similar to the subjunctive, it is in fact the direct imperative and so is quite abrupt. The actual subjunctive form (or polite imperative) would include both a subject prefix and an object infix: "Uniambie" or "Mniambie." (For more, see Wilson's Simplified Swahili, chapter 38)
I'm not a grammatics guy and I'm not fluent in Swahili, but if I understand the others' explanations correctly it is like this: some Swahili verbs require an object prefix (referring to another person), for example kuambia and kupa. I think of them as "to tell (to) someone" and "to give (to) someone". That means you can basically drop the subject prefix if you like; if there is only one prefix left, it will automatically be considered an object prefix. For example, you can say Uniambie for "(You should) tell me", but you could also drop the subject prefix and just say Niambie ("Tell me"). The object will still be yourself, since this verb is always used with an object particle.
It's an object prefix. There are more things going on here than just the difference between subjunctive and imperative. It is also the applicative form, or also called benefactive form, of 'kwamba', which means to tell or to say. Those forms would demand an indirect object to be mentioned, as it is something done for someone.
It is also still the subjunctive, but without a subject prefix it functions as a polite imperative. The simple imperative would be 'ambia'. Compare with English 'Tell me!' and 'I think that you should tell me.'