How (in)flammable is "isopropyl alcohol" really?
The Flash Point of a liquid is the minimum temperature at which a liquid gives off vapor within a test vessel in sufficient concentration to form an ignitable mixture with air near the surface of the liquid. The flash point is therefore dependent on the boiling point and consequent vapor pressure of the liquid (Source of Vapor Pressure):

$$
\begin{array}{l|c c c}
\text{Flammable Liquid} &amp; \text{Boiling Point at $\pu{1 atm}$} &amp; \text{Flash Point} &amp; \text{Vapor pressure at $\pu{25 ^\circ C}$} \\
\hline
\text{Diethyl ether} &amp; \pu{35 ^\circ C} &amp; \pu{-45 ^\circ C} &amp; \pu{532.7 mmHg} \\
n\text{-Pentane} &amp; \pu{36 ^\circ C} &amp; \pu{-40 ^\circ C} &amp; \pu{434.3 mmHg} \\
\text{Hexane} &amp; \pu{69 ^\circ C} &amp; \pu{-26 ^\circ C} &amp; \pu{151.2 mmHg} \\
\text{Ethyl acetate} &amp; \pu{77.1 ^\circ C} &amp; \pu{-4 ^\circ C} &amp; \pu{94.7 mmHg} \\
\text{Methanol} &amp; \pu{65 ^\circ C} &amp; \pu{11 ^\circ C} &amp; \pu{126.89mmHg} \\
\text{Ethanol} &amp; \pu{78 ^\circ C} &amp; \pu{12 ^\circ C} &amp; \pu{58.8 mmHg} \\\text{Isopropanol} &amp; \pu{82.2 ^\circ C} &amp; \pu{12 ^\circ C} &amp; \pu{43.6 mmHg} \\
\text{Water} &amp; \pu{100 ^\circ C} &amp; \text{N/A} &amp; \pu{23.7 mmHg} \\
\end{array}
$$

By definition, any liquid with a flash point less than $\pu{37.8 ^\circ C}$ ($\pu{100 ^\circ F}$) is considered to be a flammable liquid. Any liquid with a flash point between $\pu{100-200 ^\circ F}$ is considered combustible. In general, the relative hazard of a flammable liquid increases as the flash point decreases.

However, OP's isopropyl wipes are soaked with about 70% isopropanol and DI water (the best combination for better sanitation). For example, see these wipes on market. As a consequence, the flash point ($\approx \pu{18 ^\circ C}$) is increase on these wipes. Also, since vaporizer has good ventilation system (I assumed), these vapors never would get to saturation point in addition to combination of water and isopropanol vapors. That would reduce the flammability of vapors even with a spark (here are heating coils, I assume). That's probably why the user manual did not warn fire hazard. 

OP's question about evaporation from an open bottle: As you can see in the given table, vapor pressure of ethanol and isopropanol is quite high in room temperature ($\approx \pu{25 ^\circ C}$) compared to that of water. If bottle is open, the vapor escapes without ever getting saturated like wipes in closed box. Thus, alcohol in the bottle keep evaporate and, as a result, volume in the bottle reduces with time. On the other hand, the closed space in the box of wipes eventually get saturated with alcohol/water vapors, and evaporation stops at that point.