The timing doesn't matter: temporary HP does not stack
It doesn't matter how many different abilities the character triggers simultaneously that grant them temporary HP, they cannot be added together.
Temporary hit points aren’t cumulative. If you have temporary hit points and receive more of them, you don’t add them together, unless a game feature says you can. Instead, you decide which temporary hit points to keep. (XGE)
The fact that this rule says that they are not cumulative ever means that timing is essentially a non-issue here. You can never add temporary hit points together unless an ability says you can, even if you were able to get them at the exact same time.
D&D doesn't work when you resolve some things simultaneously
In D&D, things don't really happen at the same time. Built into the game is the unspoken assumption that things resolve one by one, in some order. In fact, you can see this plainly by the issue that you have this question. The rule for temporary HP was built around the assumption that things resolve in an order and not all at once.
A good example of how things don't work when you try to resolve things simultaneously is that there is simply no way to resolve things at times. For example, what happens when someone casts fireball on a person at the same time they are casting resist fire on themselves? Since one spell affects the other, there is no way to resolve them at the same time. Thus, the only way to do it is one at a time. Many things don't matter and can be hand waived away, but as you discovered in your question, some things are built around the idea that things are resolved one at a time and break if you try to run them the other way.1
That is why I play with (and highly recommend other tables do as well) the optional rule on simultaneous effects from Xanathar's Guide to Everything p. 77 (IMO one of the best rules they have ever added to the game).
Most effects in the game happen in succession, following an order set by the rules or the DM. In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table — whether player or DM — who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character’s turn, the player decides which of the two effects happens first.
So, the order is decided by whoever controls the character whose turn it is when multiple things trigger. They then are resolved one at a time.
In the case of temporary HP it doesn't matter regardless because the player can always choose to keep their current temp HP or swap it for new ones. In a theoretical case where the two abilities were different this would allow a character to swap their current temporary HP for a greater amount for example. However, the timing would still not matter. If things happen at the same time or one after another doesn't affect how the rules adjudicate it. They can never choose to benefit from both.
Your specific case
So, this player would get temporary hit points equal to CHA mod + warlock level (note not half the level as you stated in your question) when they reduce a creature to 0 HP. Since both trigger at the same time and give the same number of hit points, it doesn't matter which they choose. They will receive CHA mod + warlock level temporary hit points and the other ability will essentially have no effect.
1 - thank you to @thedarkwanderer for coming up with this example and working out the idea with me.