Both your example sites show an example with a separable verb but neither is clear about these verbs being separable — and worse, germanforenglishspeakers.com even gives a wrong infinitive, completely clouding that the verb is, indeed, separable.
Lies den Text vor! (Source)
The verb here is vorlesen (to read out). Note that the meaning would change if you used lesen: ‘Lies den Text!’, simply tells you to read, not to read out aloud.
Nimm die Schlüssel mit. (Source)
The verb here is not nehmen as the source claims. If it where, the meaning of the sentence would be ‘Take the keys.’ Rather, the verb is mitnehmen — ‘Take the keys with you.’ Again, this is a separable verb and moves to the end of the sentence.
Canoo.net also has an example including a separable verb, but does not label it explicitly:
Hören Sie auf. (aufhören)
The rule for this is that the imperative forms form a Verbklammer (verb bracket) just like the parts of a verb would in a normal (indicative) sentence. Typically, everything else is locate in the Hauptfeld, the bit between the two verb parts. Exceptions include infinitive constructions which, typically if longer, are often placed in the Nachfeld, i.e. after the second part. Examples:
Denk darüber nach, mitzugehen.
Komm morgen ins Kino mit.
Hör auf, solchen Stuss zu erzählen.
Fang endlich zu essen an. (Here the infinitive is short and can be pulled into the Hauptfeld. Arguably, this is not the most idiomatic way of saying this, though.)