There's probably plenty of tutorials & reference material online about puzzle design & process. Google, you know!?
Anyway, yeah... I meant to reply to this yesterday, but got side-tracked with something else (probably - I forget).
Here's some other puzzle types:
Combination of items (inventory &/or scene). Pretty self explanatory. Mix 2 or more items together to create a new item out of the existing items or to change the environment somehow, whether it's to unlock a door, knock a hole in a wall or something entirely different.
Sliding puzzles (almost everyone hates these things). These can come in 2 different forms. The first being a mini-game comprised of sliding tiles that have to be arranged to form a specific pattern or image. The second would be as objects you can slide around in a scene; let's say some boxes that obstruct your path forward. I guess things like mini-games that involve lockpicking or sliding blocks out of the way to get some object through them might also count too?
Dialog choice (timed, multi-choice, non-linear). Yes, even dialog can be a form of puzzle because your character might have to say a specific thing to obtain new information or coerce a character into saying or doing something they are reluctant to say or do. Adding a timer to important dialog choices like they do in TTG games puts the player under pressure to make a snap decision on what they think is the correct question/response, which is a useful story-telling tool; though not really relevant in the puzzle sense.
QTE (quick time events). These things are kind of hard to pull off because they sometimes make or break a game depending on how they are handled. Not everyone (like me) has great memory or hand eye coordination, which means if you make the quick time events too complicated by using complex button/click patterns or don't allow the player enough time to press the correct key or click the correct spot, then the player will end up feeling very frustrated if they have to keep playing to same bit over & over again. The QTE in TellTale's games are somewhat easy as they give the player loads of time (perhaps too much?) & not hitting the correct button doesn't seem to matter too much as I think they give you a few strikes (baseball ref) before you mess the QTE up.
There's plenty of other types of puzzles I could probably mention such as hidden objects mini-games. Match mini-games. Ring-rotation mini-game (similar to sliding tile mini-game). Control/ordering of multiple characters &/or npc to solve a puzzle. Escape the room. Text-input/combination based puzzles. Sequence memory puzzles. etc. etc.
All of which are possible in Visionaire Studio, but a large majority of them probably require scripting or complex if queries (if done with action parts, values & conditions).
Right about the follow a character puzzle you mentioned. You can use an at begin of scene action to check if the npc you are following is on scene, if they are you create a cutscene event to have npc walk to an exit then you teleport them to relevant scene. End the cutscene to give the control back to the player. Nothing too complicated.
Timed events are also not too hard to create either. You can use a value. Set it to specific time in seconds preferably then create a called by other action block that contains some action parts along the lines of this...
pause 1000ms
set value "name" - 1
if value "name" is 0
do some actions
else
jump to action part #1
end if& there you have it, a simple timed event.
As for puzzles in general, most of them are comprised of if queries, conditions & values, which is the standard basis of most things to do with game & app development. if condition is true or false - hell you're still technically asking if a returned value is true or false when you query something like if value "name" is greater than or equal to x.
Hopefully some of what I've said will be useful. I really should have created a wiki page about puzzle design ages ago, but... side-tracked.