if you last hit blue with smite, and then go the normal blue > wraiths > red route, smite will still be up in time to last hit red. its a lot better to last hit because if you're going against a good counter-jungler they can easily last hit your red and then gank you with it.
Then you got a horrible leash / guard and your team should feel bad. This is why 99.9% of the time you start the buff closest to bot lane (purple side -> blue buff, blue side -> red buff), because not only do you have more protection (mid laner + bot adc + support as compared to mid laner + top), providing the intimidation pressure to the enemy team, you get a better leash on your buff. Smiting at 1:55 means that directly afterwards you can rush to your other buff and smite it. From there, if I'm on purple side I'll go wraiths for level 3 and gank mid. On blue il go wight and gank top.
The only good time that you should start the opposite blue is in case your bot lane has a very hard lane, and wants an early (ie level 3) gank,
or if the enemy jungler is known to gank you at your second buff (ie shaco, lee sin, shyvanna); you should start the opposite one they think you're starting. Ask your team to trinket ward whichever buff you missed on and coordinate a gank if the enemy tries to steal.