POTENTIAL CONFLICT OCCURS WHEN THE PLTS OF A PA28 TRAINING FLT EXPERIENCE AN ALT EXCURSION THAT SETS OFF A TCASII TA RA ON A B737 WHEN 4 NM E OF ORL; FL.

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I RECEIVED A TKOF CLRNC TO DEPART RWY 25 AT ORL. THE TWR TOLD US TO MAKE A R DOWNWIND DEP; WITH NO MENTION OF AN ALT RESTR. I DEPARTED WITHOUT INCIDENT. ON MID FIELD DOWNWIND; TWR TOLD US TO TURN TO HDG 180 DEGS TO OVERFLY THE FIELD. TWR THEN SAID; IMMEDIATELY FOLLOWING; TO FLY HDG 090 DEGS. ABOUT 2 MINS LATER; I NOTICED MY STUDENT HAD CLBED TO 1800 FT MSL WHICH PUT US IN MCO CLASS B AIRSPACE WITHOUT CLRNC. I TOLD THE STUDENT TO DSND IMMEDIATELY. ALMOST AS SOON AS WE STARTED DSNDING; EXECUTIVE TWR ASKED US TO DSND TO 1500 FT. APPROX 3 MINS LATER; AN ACR B737 PASSED WITHIN 1/4 MI HORIZLY AND 500 FT VERTLY. EXECUTIVE TWR GAVE US NO TFA'S NOR WERE WE EVER TOLD TO CHANGE ASSIGNED HDG OF 090 DEGS AND ASSIGNED ALT OF 1500 FT MSL. UPON LNDG AT MLB; LCL CTL TOLD ME I NEEDED TO CONTACT MCO APCH. I PLACED THE PHONE CALL; AND WAS ADVISED THAT I HAD CAUSED A TCASII RA TO SOUND IN A B737 AND A PRELIMINARY DEV WOULD BE FILED. ALTHOUGH I WAS ON HDG AND ALT; I FEEL THE JET MAY HAVE BEEN TOO LOW. ADDITIONALLY; EXECUTIVE CTL TWR MAY HAVE HAD US ON A VECTOR TOO FAR S. TO PREVENT RECURRENCE; EXECUTIVE TWR SHOULD ADVISE PLTS OF ALT LIMITS IN SUCH COMPLEX AIRSPACE. ADDITIONALLY; THEY SHOULD ADVISE PLTS TO CHANGE FREQS WHEN APCHING THE LIMITS OF ORL'S CLASS D AIRSPACE.