Do modern energy saving light bulbs class as "fluorescent lighting"?
Both of the bulbs you show are fluorescent (or more specifically, compact fluorescents "CFLs"). Fluorescent bulbs are characterized by their long opaque glass tubes and the electrical ballast in the base of the bulb which controls the light. (Commercial fluorescent lighting usually has the ballast built into the fixture instead of attached to the tube, but they work the same way).

Fluorescent lighting is one type of "energy-saving" bulbs, although it's not the only kind. Other types of energy saving bulbs are LEDs (newer, more expensive than CFLs but even more efficient). Halogens are sometimes considered "energy efficient", though they're only marginally better than old-fashioned incandescents.

You might contact the manufacturer and find out what exactly is the problem with fluorescent lights. It's possible the ballasts create some electrical "noise" that the smoke alarm doesn't like. Or maybe the alarm sends a trickle of current through the fixtures which is not noticeable for incandescents but can cause fluorescent or LED bulbs to glow slightly. See also Why does using a dimmer with this ceiling fan and lights cause energy saving bulbs to flicker? and Why do my LED lights stay on, even when the switch is off? .