Multithreading - multiple users
The incorrect assuption is
If only one processor exists, then threads will run one after another.
How threads are being executed is up to the runtime environment. With java there are some definitions that certain parts of your code will not be causing synchronisation with other threads and thus will not cause (potential) rescheduling of threads.
In general, the OS will be in charge of scheduling units-of-execution. In former days mostly such entities have been processes. Now there may by processes and threads (some do scheduling only at thread level). For simplicity let ssume OS is dealing with threads only.
The OS then may allow a thread to run until it reaches a point where it can't continue, e.g. waiting for an I/O operation to cpmplete. This is good for the thread as it can use CPU for max. This is bad for all the other threads that want to get some CPU cycles on their own. (In general there always will be more threads than available CPUs.So, the problem is independent of number of CPUs.) To improve interactive behaviour an OS might use time slices that allow a thread to run for a certain time. After the time slice is expired the thread is forcible removed from the CPU and the OS selects a new thread for being run (could even be the one just interrupted).
This will allow each thread to make some progress (adding some overhead for scheduling). This way, even on a single processor system, threads my (seem) to run in parallel.
So for the OS it is not at all important whether a set of thread is resulting from a single user (or even from a single call to a web application) or has been created by a number of users and web calls.
I can talk from Java perspective, so your question is "when multiple users are accessing an application, how are the threads handled?". The answer is it all depends on how you programmed it, if you are using some web/app container they provide thread pool mechanism where you can have more than one threads to server user reuqests, Per user there is one request initiated and which in turn is handled by one thread, so if there are 10 simultaneous users there will be 10 threads to handle the 10 requests simultaneously, now we do have Non-blocking IO now a days where the request processing can be off loaded to other threads so allowing less than 10 threads to handle 10 users.
Now if you want to know how exactly thread scheduling done around CPU core, it again depends on the OS. One thing common though 'thread is the basic unit of allocation to a CPU'. Start with green threads here, and you will understand it better.
Tomcat uses Java multi-threading support to serve http requests.
To serve an http request tomcat starts a thread from the thread pool. Pool is maintained for efficiency as creation of thread is expensive.
Refer to java documentation about concurrency to read more https://docs.oracle.com/javase/tutorial/essential/concurrency/
Please see tomcat thread pool configuration for more information https://tomcat.apache.org/tomcat-8.0-doc/config/executor.html
You need understand about thread scheduler. In fact, in a single core, CPU divides its time among multiple threads (the process is not exactly sequential). In a multiple core, two (or more) threads can run simultaneously. Read thread article in wikipedia. I recommend Tanenbaum's OS book.