The question whether a German verb is "separable" (trennbar) or "non-sparable" (nicht-trannbar) is in no way connected to the English "progressive" or "continuous" form as opposed to the simple present.
The easiest way to translate an Englisch sentence built with the (present or past) progressive is using the adverb "gerade".
Das Waschbecken läuft über (always, whenever I open the faucet or do similar things, the water spills over).
Das Waschbecken läuft gerade über (right now, in this moment, the water is spillig over the topmost edge of the sink.)
In the region around the lower Ruhr river, also known as "Kohlenpott" or "Ruhrpott", there is a dialect construction known as "Ruhrpott-Verlaufsform". This construction is not proper German, but quite often used in colloquial German, and does not need any "gerade":
"Das Waschbecken ist am Überlaufen." Meaning: Just now, the water is spilling ... (as in the proper German phrase with "gerade").
There is also a past progressive form of the "Ruhrpott-Verlaufsform":
"Das Wasser war kräftig am Überlaufen, da hat einer den Hahn abgedreht, und der Spuk war vorbei."
The funny thing is that the "Ruhrpott-Verlaufsform" obeys exactly the same rules as the English present and past progressive.
There is an article in "Der Dativ ist dem Genitiv sein Tod" by B. Sick and (used to be) in "Zwiebelfisch" on the online edition of DER SPIEGEL magazine with the standard phrase:
"Dat Chantal war sisch die Haare am Fönen" (proper German:
"(die liebe) Chantal fönte sich gerade die Haare" = "dear Chantal was just dryblowing her hair", explaining the "Ruhrpott-Verlaufsform" in detail.