I found a condition where different behaviour could be observed depending on how a module is imported.

It seems to be different to write:

import module
# against:
from package import module

In the attachment you find a minimal package (imptest) with this organization:

imptest
|-> __init__.py (empty)
|-> m.py (module which initializes a variable "foo=0")
|- sub (package)
|-> __init__.py (empty)
|-> subm.py (module which, upon import, changes "m.foo=1")

And two scripts which can be directly executed:
|-> run0.py (using "import m")
|-> run1.py (using "from imptest import m")

Contents of the module m:
#########################
foo=0
def do():
global foo
foo=1
print('doing foo=',foo)
print("imported foo=",foo)

Contents of module subm:
#######################
from imptest import m
from imptest import m
print("imported sub, foo=",m.foo)

Both run0.py and run1.py imports module m and calls the do() function, thus theoretically changing foo to 1.
Both later import the subm module, which in turn imports again the m module. What I would expect is that,
since m is already in memory, it is not really imported again: so foo remains equal to 1 also after subm import.

I found that this actually depends on how I imported m in the script.

Contents of run0.py:
####################
import m
m.do()
print("importing subm")
from imptest.sub import subm

Result:
imported m; foo= 0
doing foo= 1
importing subm
imported m; foo= 0
imported sub, foo= 0

As you can see from printout "importing subm", the m module is imported again and thus foo is reset to 0. In run1.py,
I changed the line "import m" to "from imptest import m", and got the expected behaviour:

Contents of run1.py:
####################
from imptest import m
m.do()
print("importing subm")
from imptest.sub import subm

Result:
imported m; foo= 0
doing foo= 1
importing subm
imported sub, foo= 1

I know that directly running a module in the first level of a package may seem strange or not correct, but could someone explain why this is happening?
I would expect a module to be loaded in memory at the first import and then referred in any way I later or elsewhere in the program choose to import it.

Here's a simpler demo for what I believe you are experiencing:

$ mkdir package
$ cd package/
$ touch __ini__.py module.py
$ export PYTHONPATH=..
$ python3
Python 3.3.2+ (default, Feb 28 2014, 00:52:16) 
[GCC 4.8.1] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import module, package.module
>>> module is package.module
False

Even though module and package.module correspond to the same file
Python does not recognize that you intend the former to be part of a package. Your run0.py script goes through its sys.path entries and unfortunately the first entry points into a package so that all modules in that package become also visible as toplevel modules.

A good way to avoid this trap is to use relative imports

>>> from . import module
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
SystemError: Parent module '' not loaded, cannot perform relative import

This is a consequence of a script's directory getting prepended to sys.path. See issue bpo-13475.