It's raining in my terminal!
MATL, 52 bytes
xxx:&quot;1GY.Xx2e3Z@25eHG&gt;~47*cD]Xx12:~c!3G80yn-H/kZ&quot;why

Inputs are, in this order: pause between updates, number of drops, message, number of repetitions. The monitor has size 80×25 characters (hard-coded).
GIF or it didn't happen! (Example with inputs 0.2, 100, 'THE END', 30)

Or try it at MATL Online.
Explanation
xxx      % Take first three inputs implicitly and delete them (but they get
         % copied into clipboard G)
:&quot;       % Take fourth input implicitly. Repeat that many times
  1G     %   Push first input (pause time)
  Y.     %   Pause that many seconds
  Xx     %   Clear screen
  2e3    %   Push 2000 (number of chars in the monitor, 80*25)
  Z@     %   Push random permutation of the integers from 1 to 2000
  25e    %   Reshape as a 25×80 matrix, which contains the numbers from 1 to 2000
         %   in random positions
  HG     %   Push second input (number of drops)
  &gt;~     %   Set numbers that are &lt;= second input to 1, and the rest to 0
  47*c   %   Multiply by 47 (ASCII for '/') and convert to char. Char 0 will
         %   be displayed as a space
  D      %   Display
]        % End
Xx       % Clear screen
12:~     % Push row vector of twelve zeros
c!       % Convert to char and transpose. This will produce 12 lines containing
         % a space, to vertically center the message in the 25-row monitor
3G       % Push third input (message string)
80       % Push 80
yn       % Duplicate message string and push its length
-        % Subtract
H/k      % Divide by 2 and round down
Z&quot;       % Push string of that many spaces, to horizontally center the message 
         % in the 80-column monitor
w        % Swap
h        % Concatenate horizontally
y        % Duplicate the column vector of 12 spaces to fill the monitor
         % Implicitly display