Working for a lot of startups, I have seen this cycle. Really it has little to do with making the IPO look good because of number of employees, and is more about making the IPO look good because of planning for the future.
Many times an IPO is released, it will be valued at $1.00 (made up) and the market will soar and spike. Now stock shares are valued at $3.00. Great. Till after the dust settles a bit, and stocks are valued at $0.85.
This is "normal" and good. It would be better if the stocks ended a little higher than their initial value, but... such is life.
Now the initial value of the stock is made up of basically the value of the company's assets, and employees are part of those assets and its earning power. They are also a liability, but that has less impact on initial value than assets.
Sales right after IPO are based on how well a company will do. Part of that is growth. So it looks nicer to say: "We have 500 employees and have been growing by 20% per month." than to say "We have 100 employees".
In other words, before IPO, employees may be hired to make the company look like it is growing. They may be hired because the budget is projected based on expected growth and expected valuation.
After IPO, you get a concrete number. You have your budget. It may be more than you thought, or it may be less. In our example, the real budget (from capital), is only 28% of the entire projected budget, and 85% of the initial value. It's time to make some budget cuts.
Also, normally, there is a period of adjustment, company wide, as a company goes from VC funding, "here, have as much money as you want", to "real world" funding, with stricter limits and less wiggle room.