The verb to expect always takes an infinitive complement:
I expect it to rain.
They expect us to present tomorrow.
This is the normal way of forming sentences with expect. Your last example above is, as you suspected, grammatically incorrect:
*I will expect you doing well.
The other example that you gave with expect + -ing is something else. In this case., the verb working is the beginning of an adverbial phrase, and isn't a complement to expect at all.
Here's what to expect working at BigCorp.
In this sentence what to expect is a nominal relative clause indicating what you should expect, and working at BigCorp is an adverbial gerund indicating where you will be working.
Other examples can be constructed that put expect and a gerund together, but in all of those examples the gerund is not a complement to expect, but an independent grammatical phrase which just happens to come close to expect. The actual complement of expect is always an infinitive.