So you use the standard and 24 hours calendars that come with project
and set up a new one "7day" (Mon-Sun 7:00 - 18:30).
I would set the project/project information/calendar to standard and
leave it there.
Now set the 24h(offshore) and 7day(site) as TASK calendars (task
information/tab advanced/calendar) for eacht task individually if
necessary.
In the planning stage you may not know the real staff assigned, but you
could create generic resources ("engineer", "welder") and make them
available full-time (resource information/tab working time/base
calendar 24h); make sure you have the cost rates entered per hour, not
per day.
When you assign those unlimited generic resources, your tasks should
schedule according to their task calendar (Site or offshore if chosen
in task information, with standard if "none" in task information).
That should give you the information you're looking for in overall
schedule and cost.
Now moving into detailed assignment you replace the generic resources
with real people, and you'll have to use the resource calendars and
replace one generic "24" hour engineer by assigning one "12h
nightshift" and one "12h dayshift" each. Project won't change schedule
or cost because in sum they still represent a "24h engineer". Going
into more detail and individual calendars ("engineer Johnny B") will
help you when you're in progress and want to see the effect of
individual off-times (Johnny B broke leg, non-working for the rest of
the week).
If you're using the calendars this way - what is the unexpected
behaviour?
Can you give examples that we can reproduce, say on a task (calendar a)
with x work, y duration, start s, finish f; task assignments z with
resource calendar b...
I know that's a lot of details, but then project simply has all those
parameters to play with...