Is it right to say that fluorescent lamps are actually fluorescent?
Fluorescent lamps do primarily work by fluorescence. According to this Wikipedia article:  


  "The inner surface of the lamp is coated with a fluorescent (and often slightly phosphorescent) coating..." 


First off, an electric current excites the outer electrons of gas atoms (typically mercury) within the lamp to a higher energy state. When the atoms relax back to their stable state, UV light is emitted. This UV light is then absorbed by a fluorescent material coating the inside of the lamp, which in turn fluoresces in the visible region of the EM spectrum. Some confusion could arise here as this coating is called a phosphor, even though the type of luminescence is fluorescence, not phosphorescence. 

The rate at which the luminescence occurs is not important because there is a continuous supply of electric current. If it were necessary to provide light for any significant period of time after the power source was removed, then some type of phosphorescence would be necessary due to it's much longer lifetime as compared to fluorescence, as you pointed out. However, this is clearly not a requirement for a standard fluorescent lamp.