Is there a way to hint to query optimizer to MySQL which constraints should be done first?
I have rather bad news for you in this regard
MySQL Query Optimizer tends to stray away for further optimization once it sees a FULLTEXT index. I have written about this before in the StackExchange

May 23, 2011 : https://stackoverflow.com/a/6092216/491757
Oct 25, 2011: FULLTEXT index ignored in BOOLEAN MODE with &#39;number of words&#39; conditional
Jan 26, 2012 : Mysql fulltext search my.cnf optimization
May 07, 2012 : MySQL EXPLAIN doesn&#39;t show &#39;use index&#39; for FULLTEXT

You will have refactor the query
My suggestion would be to do the one of the following
SUGGESTION #1

Retrieve Business IDs suing the FULLTEXT Search
Perform GeoSpatial Search on the Retrieved IDs

SUGGESTION #2

Retrieve Business IDs using GeoSpatial Search (Since you said it take 0.9 seconds)
Perform the FULLTEXT Search on the GeoSpatial-Retrieved Businesses IDs

SUGGESTION #3

Retrieve Business IDs using GeoSpatial Search (Since you said it take 0.9 seconds) in Subquery1
Retrieve Business IDs using FULLTEXT Search in Subquery2
INNER JOIN Subquery1 and Subquery2

SUGGESTION #4

Retrieve Business IDs using GeoSpatial Search (Since you said it take 0.9 seconds)
DO NOT USE FullTextSerach. Use REGEXP against GeoSpatial-Retrieved Businesses IDs

Here is your original query:
SELECT BusinessID as ID,  
    111151.29341326*SQRT(pow(-6.186751-X(LatLong),2)+
    pow(106.772835-Y(LatLong),2)*0.98838574205337) AS Distance
from tableauxiliary 
USE Index (LatLong_2,FullTextSearch)
WHERE
    MBRContains(
    GeomFromText (
        'MULTIPOINT(-6.1934985598076 106.76604791159,-6.1800034401924 106.77962208841)'
        ),
        Latlong)  
    AND Prominent &gt;15 
    AND MATCH FullTextSearch AGAINST ('a*' IN BOOLEAN MODE)
    ORDER BY
  Distance;

If the MySQL Query Optimizer detects a FULLTEXT search along with the conjunction AND followed by an expression within the same WHERE clause (thus, the same level of evaluation within an EXPLAIN plan), the MySQL Query Optimizer will take a vacation after working with the FULLTEXT search.
Perhaps you could try something like this (from SUGGESTION #1):
SELECT BusinessID as ID,  
    111151.29341326*SQRT(pow(-6.186751-X(LatLong),2)+
    pow(106.772835-Y(LatLong),2)*0.98838574205337) AS Distance
FROM
(
    SELECT BusinessID,LatLong
    FROM
    (
        SELECT BusinessID,Prominent,LatLong
        From tableauxiliary WHERE
        MATCH FullTextSearch AGAINST ('a*' IN BOOLEAN MODE)
    ) AA
    WHERE Prominent &gt; 15
) A
WHERE
    MBRContains(
    GeomFromText (
        'MULTIPOINT(-6.1934985598076 106.76604791159,-6.1800034401924 106.77962208841)'
        ),
        Latlong)  
ORDER BY
    Distance
;

Notice you do not see the conjunction AND. Please check the EXPLAIN plan for this. The query should do the following:

Gather BusinessID,Prominent,LatLong That Matched the FULLTEXT search
Remove BusinessID,LatLong Whose Prominent value is &lt; 15
Check Distance of remaining BusinessID values
sort the Check Distance results by Distance

UPDATE 2012-08-08 11:30 EDT
As stated earlier, the FULLTEXT index seems to abandon all hope of using other indexes. Perhaps two subqueries that are JOINed (SUGGESTION #3)
SELECT BusinessID as ID,  
    111151.29341326*SQRT(pow(-6.186751-X(LatLong),2)+
    pow(106.772835-Y(LatLong),2)*0.98838574205337) AS Distance
FROM
(
    SELECT BusinessID,Prominent From tableauxiliary WHERE
    MATCH FullTextSearch AGAINST ('a*' IN BOOLEAN MODE)
) A
INNER JOIN
(
    SELECT BusinessID From tableauxiliary WHERE
    MBRContains(
    GeomFromText (
        'MULTIPOINT(-6.1934985598076 106.76604791159,-6.1800034401924 106.77962208841)'
        ),
        Latlong)
) B
USING (BusinessID)
WHERE Prominent &gt; 15
ORDER BY
    Distance
;

You may want to abandon using FULLTEXT searching altogether and try regular expressions (SUGGESTION #4)
SELECT B.BusinessID as ID,  
    111151.29341326*SQRT(pow(-6.186751-X(B.LatLong),2)+
    pow(106.772835-Y(B.LatLong),2)*0.98838574205337) AS Distance
FROM
(
    SELECT BusinessID From tableauxiliary WHERE
    MBRContains(
    GeomFromText (
        'MULTIPOINT(-6.1934985598076 106.76604791159,-6.1800034401924 106.77962208841)'
        ),
        Latlong)
) A INNER JOIN tableauxiliary B USING (BusinessID)
WHERE B.Prominent &gt; 15 AND
((B.FullTextSearch REGEXP ' a*') OR (B.FullTextSearch REGEXP '^a*'))
ORDER BY
    Distance
;