Hebrew, as you know, is a right-to-left language and, when used in combination with left-to-right languages such as English, provides bidirectional formatting of text.
Unicode stores text in a logical order. That is, the characters are stored left-to-right in the order in which they are typed even though the end-user is seeing the text right adjusted and flowing left.
CCSID 424 stores text in visual order. That is, the characters are stored right-to-left in the order in which they are typed and seen by the end-user.
When you are "moving" the data from the Unicode variable to the alphanumeric variable the system is converting the Hebrew data from logical order to visual order (due to the CCSID differences). The first character in an 'English only' line has a left-to-right orientation and so the visual text starts at the left. The first character in a 'Hebrew only' line has a right-to-left orientation and so the visual text starts at the right. A line of text containing both English and Hebrew would have it's orientation set by the initial logical character encountered (that was not neutral in terms of orientation). Visually the Hebrew text should be where you are finding it in the storage associated with the alphanumeric variable. This is obviously "different" from what you expected, though it is "correct".
A question for you. How is the Hebrew data, in alphanumeric form, being used by your application? Logical ordering is generally the preferred approach for any type of processing (as opposed to visual, which is a pain for sorting, etc), in which case you may want to delay when you convert to visual form. Normally you would convert to a visual CCSID such as 424 only for display/print purposes, in which case the user should be seeing what they would expect (right-to-left Hebrew text).
Depending on what you are trying to do, other EBCDIC CCSIDs are available and will provide a left adjusted result -- but they will also leave the Hebrew data in logical order (that is, not suitable for direct display or print). These other CCSIDs are 62211, 62235, and 62245.
To be able to help, more information is really needed on what the problem is.