Remember that tuning is tension . . . that is, a given string tuned to a certain pitch on a given scale length cold be expressed in lbs./ft. to get that pitch.
More tension is sharp. Less tension if flat, referenced to the original tuned pitch. This is REAL important in the piano business, as the total tension on your average 9-foot concert grand is around 60,000 lbs: No wonder the harps are all X-Rayed to check the metallurgy. In the old days, these would occasionally experience sudden deformation, could really ruin your day !
So, for a fretted note to go flat on a string that strobes open 'in pitch' would make me look for one of two things:
First, never trust your strings. Bad winding in the string itself. Incorrect winding around the post. Wrong scale strings. If I understand you recently bought this bass, are these the same strings that have been on it who knows how long in the store? If they are, throw them out. Use your string-du-jour, then see what happens.
Second, the bass would have to be letting it go flat. Unique to Alembics: Are the adjustable nut screws snug, especially on the E side?
Is the E just enough to big for the nut slot to go flat once you begin to play after you play, is their good clearance? Is the saddle/bridge assembly snug, all the screws?
For my own two cents, until you install new strings in your preferred brand of the right scale length and gauges for your bass, there are LOTS of blind alleys to get lost in using old strings to diagnose this.
J o e y