Like 뱨 pronounced "pae" instead of "pyae" and then 뵤 as "pyo" instead of "po." How to ionized vowels
I just don't know why some have the ionized vowel sounds and some don't. I need help.

Question

Answer

You are wrong.
뱨 is pronounced as /pyae/
뵤 is pronounced as /pyo/
배 is pronounced as /pae/
보 is pronounced as /po/

Only after ㅈ,ㅊ, the vowel sound ionize(?).
재,쟤 are pronounced as /jae/
조,죠 are pronounced as /jo/ 
채,챼 are pronounced as /chae/
초,쵸 are pronounced as /cho/

BTW, '계, 례, 몌, 폐, 혜' are allowed to pronounce as [게, 레, 메, 페, 헤]
핑계     ->     핑게 
계시다 ->  게시다 
폐품(廢品) -> 페품

Here is the list of vowels
ㅏ	아	IPA [a̠]
ㅑ	야	IPA [ja̠]
ㅓ	어	IPA [ʌ̹]
ㅕ	여	IPA [jʌ̹]
ㅗ	오	IPA [o̞]
ㅛ	요	IPA [jo]
ㅜ	우	IPA [u]
ㅠ	유	IPA [ju]
ㅡ	으	IPA [ɯ]
ㅣ	이	IPA [i]
ㅐ	애	IPA [ɛ̝]
ㅒ	얘	IPA [jɛ̝]
ㅔ	에	IPA [e̞]
ㅖ	예	IPA [je̞]
ㅘ	와	IPA [wa̠]
ㅙ	왜	IPA [wɛ̝]
ㅚ	외	IPA [ø̞ / we̞]
ㅝ	워	IPA [wʌ̹]
ㅞ	웨	IPA [we̞]
ㅟ	위	IPA [ɥi / y]
ㅢ	의	IPA [ɰi]

Answer

Actually,  뱨 is more like bae, and 폐 is pae.  Koreans often mix them up when writing in English, eg: Pusan ('Busan') , Hankook Tyres ('Hangook' - as a final sound, g sounds like k).  It happens in Chinese too; Taipei ('Taibei').  I don't know why.. maybe they're just not very familiar with English sounds..
:)