Your question isn't real clear, but lets get clear on how the Create Random Points tool works with a constraining feature class.
From the help:
Random points will be generated inside or along the features in this
feature class. The constraining feature class can be point,
multipoint, line, or polygon. Points will be randomly placed inside
polygon features, along line features, or at point feature locations.
Each feature in this feature class will have the specified number of
points generated inside it (for example, if you specify 100 points,
and the constraining feature class has 5 features, 100 random points
will be generated in each feature, totaling 500 points).
This is pretty straight forward. From your question, what is not clear is if you're running into the "issue" of how the tool will put the asked for number of points into each feature, vs the entire feature class. You could run the Dissolve tool to collapse all the individual features into a single-feature polygon. With this feature class, provide it to the Random Points tool as the Constraining Feature Class
The other possible "issue" is you've used the Constraining Extent parameter with your feature class. If this is the case, you'll absolutely run the chance of having points fall outside your feature class boundaries. For example, the extent of a circle is a square; points could call inside or outside the circle boundary. Simple, this is not the right parameter for what you want to do.