How does Frequency-division multiplexing deals with overlaps?
As some people said in the comments, you are misunderstanding what frequency division multiplexing means. 

FDM does not mean that each channel sends data at different times (or with different intervals separating chunks of data being sent).

FDM means that each channel sends data by using a different band of the frequency spectrum. 

In a simple example, channel n might send a message \$m_n(t)\$ by sending a signal

$$v_n(t)=A\left(1+m_n(t)\right)\sin\left(2\pi{}f_n t\right)$$

Notice that this signal doesn't turn off and on at different times. It is continuously present. 

Again, using a simple example rather than a practical one, each of the different signals could be picked out at the receiver using a bandpass filter centered around \$f_n\$, allowing each of the signals in the system to be recovered independently.