Strange effect of distributed inflows

I have a two water body model with spillway gates between the water bodies and am trying to achieve a good water balance. However, there are many cases where I have spilling occurring from one water body to the other which the water balance utility appears to have trouble dealing with. I have been trying to develop my own script to accomplish the water balancing, but have had problems figuring out what sorts of inputs generate the desired output.

This lead me to try a little experiment. I set all of my inflows and outflows to 0 so that I have a steady pool of water (in both water bodies). I then added a single pulse of 10 m^3/sec on a single time step in my water balance file (which is in hourly timesteps) as a distributed inflow. What I was surprised to find out is that the water surface elevation began to rise BEFORE the timestep that I actually added the water.

The Water balance timesteps and the model output timesteps are the same, so I am skeptical that this is a linear interpolation issue between different timesteps.

This is a snip of the output I am getting. I tested the model without any distributed inflow and had a constant pool elevation of 315.35, so I know there are no other inputs/outputs in the model.

Jday WS Elevation
2.792 315.35
2.833 315.35
2.875 315.35
2.917 315.3533
2.958 315.3567
3.000 315.36
3.042 315.3633
3.083 315.3667
3.125 315.37
3.167 315.37
3.208 315.37
3.250 315.37

As you can see above (simulation results) show a water level increase before the only inflow to the system (on Julian day 3 from the table below).

Jday m^3/sec
2.792 0
2.833 0
2.875 0
2.917 0
2.958 0
3.000 10
3.042 0
3.083 0
3.125 0
3.167 0
3.208 0
3.250 0

What I don't understand is why I am seeing the water level raise on Jday 2.917 when the inflow should be 0. Jday 2.958 water surface raise might be understandable as there are computational timesteps between Jday 2.958 and Jday 3.000 which would cause a linear interpolation from 0 cfs to 10 cfs of inflow. However Jday 2.917 to Jday 2.958 should all interpolate to 0, so the result is very surprising to me.